Figure 9a

Figure 9b

I here report the consolidation of this program, also thanks to the involvement of all the IRAP-PhD students (see Fig. 9b). I will review here just a few topics, which will also be presented in the oral contributions of this Scientific Meeting.

Particularly important is the report on Gamma-rays and Neutrinos from Cosmic Accelerators, on Page 1, which summarizes the activities traditionally carried on by the ICRANet Armenian Scientists in the MAGIC and HESS collaborations. The evolution and future prospects on the analysis of the high-energy emission for GRBs are presented in this report by Prof. Aharonian and Dr. Sahakyan. In parallel, in 2013 has been completed the coating of the telescope in the .Byurakan Observatory, which will give a crucial support to the GRB-SN follow-up observations traditionally addressed as afterglow.

The topic of BKL cosmology is one of the most important and classical contributions of Einstein theory to the study of cosmology. This classic work, developed by Belinski, Kalatnikov and Lifshitz, has already been reviewed in all the major treaties on general relativity, but only recently a new insight has come from the impressive discoveries made by Thibault Damour at the IHES in Paris, by Prof. Mark Henneaux at the University of Bruxelles, and by Herman Nicolai at the Albert Einstein Institute in Potsdam, on the way to generalize the BKL theory of cosmological singularity to the string theories. The new results can be of essential importance for understanding the problem of cosmological singularity and for the identification of hidden internal symmetries in fundamental physics. Prof. Belinski has already finished his part of a new book on “Cosmological singularities” which will written in co-authorship with Prof. Damour. The book has planned to be published by Cambridge University Press. A shortened and adapted version of this book has already been presented in the AIP conference proceedings of XIV Brazilian School of Cosmology and Gravitation (V. Belinski “On the Singularity Phenomenon in Cosmology”, in: Chapter 2, Cosmology and Gravitation: XIV Brazilian School of Cosmology and Gravitation, Cambridge Scientific Publishers, 2011). Three graduate students of the IRAP PhD program are actually working on this topic for their theses with Profs. Hagen Kleinert and Hermann Nicolai in Berlin (Dutta, Fleig, and Gruber). Among the completely new results achieved during the last year, first it should be mentioned the exact description of the quantum dynamics of a supersymmetric version of the Bianchi IX cosmological model and identification the basic role of the Kac-Moody algebra in the structure of the quantum Hamiltonian (T.Damour et al.). The second result is the proof of the existence of the general cosmological solution with the Friedman initial singularity if the influence of the dissipative processis near singularity will be taken into account in the framework of the Israel-Stewart theory (V.Belinski).

On a different topic, during the last year the solitonic solutions of GR has received new interest in respect of the exact solutions of Einstein and Einstein-Maxwell equations: a) The old problem how to generate the exact stationary axisymmetric solutions corresponding to the charged masses with horizons in the framework of Inverse Scattering Method (ISM) was investigated. It was shown that applicability of the ISM in presence of electromagnetic field is not restricted only to the cases with naked singularities (as it have been erroneously stated by some authors). In fact solutions of Einstein-Maxwell equations with horizon also follows from ISM and they are of the same solitonic character. The mathematical procedure of analytical continuations of the naked-singularity solitonic solutions in the space of their parameters which procedure results in solitonic solutions with horizon has been described (G. Alekseev and V. Belinski “Soliton Nature of Equilibrium State of Two Charged Masses in General Relativity”, arXiv:gr-qc/1103.0582, IJMP(D) in press, 2011); b) It was found the new way of derivation of the Kerr solution by adding to the Schwarzchild black hole the solitonic vortex made from the pure gravitational field. With this method, one can figure out how rotational energy can contribute to the mass of the resulting Kerr black hole. Also the relation of the Hanson-Regge type between the mass and angular momentum of a Kerr black hole has been established and its connection with the Christodoulou-Ruffini concept of irreducible mass was analyzed (V. Belinski and H. W. Lee “Kerr rotation as solitonic whirl around Schwarzschild black hole”, Nuovo Cimento, submitted, 2011). During the last year all these constructions was generalized also for the electrically charged black holes. It was shown how one can derive the Kerr-Newman solution by adding a solitonic vortex to the Reissner-Nordstrom black hole. The report is on Page 53.

The report on Gamma-Ray Bursts starts on page 71. Major progresses have been accomplished this years in the following aspects (see Figs. 10-18):

1) Particularly exciting is the new possibility of having components yet to be observed in GRB sources. In fact, we have shown that it is not possible to interpret GRB 090618 and GRB 101023 within the framework of the traditional single component GRB model. We argue that the observation of the first episode of duration of around 50s could not be a part of a canonical GRB, while the residual emission could be modeled easily with the models existing in literature. This led to the definition of the novel concept of “protoblack hole emission”.

2) Thanks to this new understanding, we studied the X-ray emission shown by GRBs associated to SNe as due to the newly born neutron star, introducing the concept of the “neo neutron stars” and further developing the Induced Gravitational Collapse (IGC) scenario. This led us on May 2^nd to predict, from the observations of the prompt emission of GRB 130427A, the occurrence of an associated supernova between May 10^th and May 13^th. This prediction has been indeed confirmed by the observations. This field is evolving so rapidly that “usual” publications in Scientific Journals are no longer fast enough to keep pace. We therefore issued a number of GCN Circulars to quickly inform the Scientific Community of the discoveries:

-) GCN 14526: “GRB 130427A: Predictions about the occurrence of a supernova”;

-) GCN 14888: “GRB 130609B: Theoretical redshift estimation”;

-) GCN 14913: “GRB 130603B: Analogy with GRB 090510A and possible connection with a supernova”;

-) GCN 15322: “GRB 130925A: Possible signatures of binary nature in the afterglow - Request for observations”;

-) GCN 15560: “GRB 060614: theoretical derivation of the redshift and need for deeper search of the host galaxy”;

-) GCN 15576: “GRB 131202A: theoretical estimation of the redshift”.

3) The new developments of the IGC scenario led us to explore the possibility to introduce a new redshift estimator, which we called “cosmic candle by a binary driven hypernova”, for members of the subclass of IGC-GRBs.

4) We identified the first example of genuine short GRBs and we identified the new class of GRBs “disguised by excess”. Particularly interesting is also the possible collaboration with Brazil on space projects

 
Figure 10: A candidate Genuine Short GRB - Figure 11: Spectrum of the genuine short

 
Figure 12: GRB 090618 light curve - Figure 13: GRB 101023 light curve

 
Figure 14: Temperature evolution in Episode 1 of GRB 090618 - Figure 15: Radius evolution in Episode 1 of GRB 090618

 
Figure 16: An universal behaviour of rest-frame X-ray luminosity after 20.000 - Figure 17: The nested structure of GRB-SN X-ray afterglows

Figure 18: Arnett and Meakin 2D computations of core collapse

In the report “Relativistic effects in Physics and Astrophysics” (see page 553) it is studied the distribution of the GRB bolometric luminosity over the EQTSs, with special attention to the prompt emission phase. We analyze as well the temporal evolution of the EQTS apparent size in the sky. We use the analytic solutions of the equations of motion of the fireshell and the corresponding analytic expressions of the EQTSs which have been presented in recent works and which are valid for both the fully radiative and the adiabatic dynamics. We find the novel result that at the beginning of the prompt emission the most luminous regions of the EQTSs are the ones closest to the line of sight. On the contrary, in the late prompt emission and in the early afterglow phases the most luminous EQTS regions are the ones closest to the boundary of the visible region (see Fig. 19). We find as well an expression for the apparent radius of the EQTS in the sky, valid in both the fully radiative and the adiabatic regimes. Such considerations are essential for the theoretical interpretation of the prompt emission phase of GRBs.

Figure 19: Evolution of luminosity over the EQTSs

The collaboration on Supernovae is mainly centered from almost daily scientific contact with Prof. Massimo Della Valle, who is currently PI of a VLT proposal “A spectroscopic study of the supernova/GRB connection”. A short summary of the internationally well-known activities of Prof. Della Valle, who is an Adjunct Professor at ICRANet, is given in the report on page 2175, which contains the many publications in international journals. Prof. Della Valle is also very actively following one graduate student of the IRAP PhD program. A new stimulus has come from the recent understanding of the IGC paradigm, which allows a completely new understanding of the relation between the supernovae and the GRBs

The Report on “Cosmology and Large Scale Structures” on page 621, led by Prof. Fang LiZhi, manifests the progress made by the ICRANet group at the University of Arizona. It deals with three different topics. A. Turbulence behavior of cosmic baryon gas. With hydrodynamic simulation sample of the LCDM universe produced by the WENO algorithm, we show that the intermittency of the velocity field of cosmic baryon fluid at redshift z=0 in the scale range from the Jeans length to about 16h^-1 Mpc can be extremely well described by the She-Lévĕque's scaling formula, which is used to describe a fully developed turbulence. We also found that the non-Gaussian features of the cosmic baryon fluid and Ly-a transmitted flux of quasar absorption spectrum can be well described by a log-Poisson hierarchy. B. Wouthuysen-Field coupling. With a state-of-the-art numerical method, we show that the resonant scattering of Ly-a photons with neutral hydrogen atoms will lock the color temperature of the photon spectrum around the Ly-a frequency to be equal to the kinetic temperature of hydrogen gas. The time scales of the onset of Wouthuysen-Field coupling, the profile of frequency distribution of photons in the state of local thermal equilibrium, the effects of the expansion of the universe on the Wouthuysen-Field coupling in a optical thick halos have also been found. These results are essential for studying the 21 cm signal from high redshift sources. C. Time-dependent behavior of Lya photon transfer. Lya photons have been widely applied to study cosmological problems in high redshifts. Since the time scales of high redshift sources, such as GRBs, generally are short, time-dependent solutions of Lya photon transfer becomes serious. However, no reliable numerical solvers of the time-dependent problem of radiative transfer equation with resonant scattering have been developed till 2006. The time-dependent solver (Meiksin, MN, 370, (2006), 2025-2037) still cannot pass the test of analytical solutions (Field, ApJ, 129, (1959), 551). The solver based on the WENO scheme has been established. It can very well pass various tests (Roy et al ApJ, 716, 2010, 604). It reveals many interesting features of the time evolution of resonant photons Lya in optical thick medium. It provides the solutions of studying the time-dependent effect of resonant scattering on the profile of red damping wing of GRBs. It is crucial to understand the halos of GRBs. This report is going to be updated thanks to the new contributions of Prof. XiaoHui Fan.

The Report “Theoretical Astroparticle Physics” on page 671 represents the summary of activities during the last year on this topic by the group including: Carlo Luciano Bianco, Remo Ruffini, Gregory Vereshchagin, She-Sheng Xue. Students working within the group include: Alberto Benedetti, Micol Benetti, Damien Begue, Ivan Siutsou. Astroparticle physics is a new field of research emerging at the intersection of particle physics, astrophysics and cosmology. We focused on several topics with three major directions of research: a) electron-positron plasma, b) transparency of relativistically expanding plasma and GRBs, c) neutrinos and large scale structure formation in cosmology, d) the role of dark matter in galaxies and its cosmological counterpart and e) cosmological data and indications for new physics. Electron-positron plasma appear relevant for GRBs and also for the Early Universe, in laboratory experiments with ultraintense lasers, etc. We examine quantum corrections to the collision integrals and determine timescales of relaxation towards thermal equilibrium for high temperature electron-positron-photon plasma. (A.G. Aksenov, R. Ruffini. I.A. Siutsou and G.V. Vereshchagin, “Bose enhancement and Pauli blocking in the pair plasma”, in preparation). We investigate the behaviour of the electron-positron pairs created by a strong electric field. We show how the energy conversion from initial electric field to thermal electron-positron plasma occurs in a complicated sequence of processes starting with Schwinger pair production which is followed by oscillations of created pairs due to back reaction on initial electric field, then production of photons due to annihilation of pairs and finally isotropization of created electron–positron–photon plasma (A. Benedetti, R. Ruffini and G.V. Vereshchagin, “Phase space evolution of pairs created in strong electric fields”, Physics Letters A, Vol. 377 (2013) 206–215). We also consider analogies and differences of physical conditions of electron-positron plasma in GRBs and in cosmology. (R. Ruffini and G.V. Vereshchagin, ”Electron-positron plasma in GRBs and in cosmology”, Il Nuovo Cimento C, Vol. 36, Issue 1, (2013) pp.255-266). We study the photospheric emission from ultrarelativistic outflows, which is relevant for understanding GRB emission when ultrarelativistically expanding plasma becomes optically thin. In order to find the observed spectrum we proceed in several different directions: a) approximations to the radiative transfer equations (R. Ruffni, I. A. Siutsou and G. V. Vereshchagin, ”Theory of photospheric emission from relativistic outflows”, the Astrophysical Journal, Vol. 772, Issue 1 (2013) article id. 11) b) Monte Carlo simulations of photon scattering at the dynamical ”photosphere” (D. Begue, I. A. Siutsou and G. V. Vereshchagin, ”Monte Carlo simulations of the photospheric emission in GRBs”, the Astrophysical Journal, Vol. 767, Issue 2 (2013) article id. 139); c) Kompaneets equation with anisotropic photon field (A.G. Aksenov, R. Ruffni and G. V. Vereshchagin, ”Comptonization of photons near the photosphere of relativistic outflows”, MNRAS Letters, Vol. 436, Issue 1 (2013) pp. L54-L58) and d) relativistic Boltzmann equations (A. Benedetti and G.V. Vereshchagin, in preparation, 2013). All these results indicate that the photospheric spectrum from ultrarelativistic sources is wider than the Planck one, see Figure 20. In particular, we found α=-1, as typically observed in GRBs for temperature decreasing inversely proportional to radius squared.

Figure 20. The spectrum of photospheric emission from photon thick outflow obtained with different approximations. Dotted curve shows the Planck spectrum. Dashed-dotted curve shows the result from Ruffini et al. (2013b) obtained using the fuzzy photosphere approximation. Dotted curve shows the result from Begue et al. (2013) obtained from Monte Carlo simulations. Solid curve shows the result from Aksenov et al. (2012) obtained by the solution of the radiative transfer equation with the Fokker-Planck approximation to the collision integral.

In the framework of cosmology we show that in modelling the distribution of dark matter in galaxies in terms of equilibrium configurations of semi-degenerate self-gravitating fermions, it allow us to determine a novel core-halo morphology for the dark matter density profiles, as well as an associated novel particle mass bound in the keV range. The most general core-halo solution presents a segregation of three new physical regimes: 1) an inner core governed by a degenerate quantum state of the ‘inos’. 2) At larger radii a low degenerate physical regime exist with a sharply decreasing density distribution followed by an extended plateau. 3) Finally a third regime in which the fermions follow the classical Boltzmann statistics with flat rotation curves. We further check the predicted circular velocity profiles against a sample of high quality rotation curves obtained from recent observations by The HI Nearby Galaxy Survey (THINGS). After extraction of ordinary matter contributions (stellar disk, bulge and gas), we obtain the rotational curves purely due to dark matter and fit with our rotational velocity profiles and with Einasto profiles by least square method. We find that, for the larger part of the sample corresponding to cored

(i.e. not cuspy) Einasto curves, our model is preferred in the majority of the cases. Another relevant observational aspect we consider to check on galactic halos, is the so called Universality laws. This law found by Donato et. al. (2009) implies a constant acceleration due to dark matter at a given halo radius, and is valid for a wide range of galaxies, ranging from dwarf to ellipticals. We then show that it always exists a given set of the free parameters of our model (with ‘ino’ masses beyond the lower bound previously found) which is in agreement with this observational universal result. More observational data coming from the center of some galaxies (i.e. the compact region in the center of our galaxy Sgr A*), compels us to study an extension within the model which includes a new interaction (other than gravitational) between the ‘inos’. For this aim, the minimal standard model extension candidate for dark matter, i.e. the sterile neutrino is considered. The fact that the keV-mass range for the sterile neutrinos be in agreement with all current astrophysical/cosmological constraints makes it an excellent candidate. We present future perspectives on how this generalized model of interacting self-gravitating fermions may deal with the distribution of dark matter in galaxies at all scales, from the very center up to the outer halos in a self-consistent way. Cosmological data and indications for new physics: This year we work on constraint cosmological parameters starting from the minimal model ΛCDM called Harrison-Zel'dovich (HZ) model and increasing the number of parameters going to explore several interesting models.

The most important metrics in general relativity is the Kerr-Newman solution which describes the gravitational and electromagnetic fields of a rotating charged mass, characterized by its mass M, charge Q and angular momentum L in geometrical units. This solution characterizes the field of a black hole. For astrophysical purposes, however, it is necessary to take into account the effects due to the moment of inertia of the object. To attack this problem, an exact solution of the Einstein-Maxwell equations have been proposed by Mashhoon and Quevedo which posses an infinite set of gravitational and electromagnetic multipole moments. It is not clear, however, how this external solution to an astrophysical object can be matched to a physical internal solution corresponding to a physically acceptable rotating mass. The report “Generalization of the Kerr-Newman solution” on page 1031 reports on current progresses in using an explicit solution of the Hartle-Thorne equation to an eternal solution with N independent quadrupole moments. Equally important has been the result recently obtained by Belvedere showing that a fast rotating model of neutron star with global charge neutrality within the Hartle-Thorne approximation leads to an internal solution of the Kerr metric.

The Report from ICRA-BR on page 1157 covered a wide range thematic in cosmology and non linear relativistic field theory studied by Prof. M. Novello and his group. This include the geometrical description of quantum mechanics where it is shown that quantum mechanics could be interpreted as a modification of the euclidean nature of a 3D space into a particular affine space. In this formulation, deformation of physical distances are in the core of quantum effects allowing a geometrical formulation of the uncertainty principle. Prof. Novello also studied the Higgs mechanism without Higgs boson. The purpose of this work is to show that the gravitational interaction is able to generate mass for all body. A main part of his activity is related to bouncing cosmology.

The report on Black Holes and Quasars refers to the activity of Prof. Brian Punsly (see page 1171), who is actively participating within ICRANet with the publication of his internationally recognized book on “Black hole gravitohydromagnetics”, the first and second edition (2010) being published with Springer. In addition, Prof. Punsly have been interested in observational properties of quasars such as broad line emission excess in radio loud quasars accentuated for polar line of sight and excess narrow line widths of broad emission lines in broad absorption line quasars, showing that this is best explained by polar lines of sight.

The problem “The electron-positron pairs in physics and astrophysics: from heavy nuclei to black holes” has been the subject of a physics reports of more than 500 references, which is inserted on page 1351, by Ruffini, Vereshchagin and Xue. There, all the different aspects of the field has been reviewed: The fundamental contributions to the electron-positron pair creation and annihilation and the concept of critical electric field; Nonlinear electrodynamics and rate of pair creation; Pair production and annihilation in QED; Semi-classical description of pair production in a general electric field; Phenomenology of electron-positron pair creation and annihilation; The extraction of blackholic energy from a black hole by vacuum polarization processes; Plasma oscillations in electric fields; Thermalization of the mildly relativistic pair plasma. Due to the interaction of physics and astrophysics we are witnessing in these years a splendid synthesis of theoretical, experimental and observational results originating from three fundamental physical processes. They were originally proposed by Dirac, by Breit and Wheeler and by Sauter, Heisenberg, Euler and Schwinger. For almost seventy years they have all three been followed by a continued effort of experimental verification on Earth based experiments. The Dirac process, e⁺e →2 g, has been by far the most successful. It has obtained extremely accurate experimental verification and has led as well to an enormous number of new physics in possibly one of the most fruitful experimental avenues by introduction of storage rings in Frascati and followed by the largest accelerators worldwide: DESY, SLAC etc. The Breit-Wheeler process, 2g → e⁺e^-, although conceptually simple, being the inverse process of the Dirac one, has been by far one of the most difficult to be verified experimentally. Only recently, through the technology based on free electron X-ray laser and its numerous applications in Earth-based experiments, some first indications of its possible verification have been reached. The vacuum polarization process in strong electromagnetic field, pioneered by Sauter, Heisenberg, Euler and Schwinger, introduced the concept of critical electric field. It has been searched without success for more than forty years by heavy-ion collisions in many of the leading particle accelerators worldwide. In view of the recent developments in the free electron lasers, we have invited at ICRANet Prof. John Madey, the inventor of the free electron lasers, to give a set of lectures and to explore the possibility to have, by focusing the free electron laser signals, the realization in the laboratory of the Breit-Wheeler process. Prof. Madey has also accepted the position of Adjunct Professor at ICRANet, and he is planning a collaboration with us in the forthcoming years.

In the report on page 1181, using the formula obtained for the rate of pair production in spatially varying external electric field dynamical equations describing the space and time evolutions of pair-induced electric charges, currents and fields bounded within a given spatial region are solved. These results imply the wave propagation of the pair-induced electric field and wave-transportation of the electromagnetic energy in the strong field region. Analogously to the electromagnetic radiation emitted from an alternating electric current, the space and time variations of pair-induced electric currents and charges emit an electromagnetic radiation. We show that this radiation has a peculiar energy-spectrum that is clearly distinguishable from the energy-spectra of the bremsstrahlung radiation, electron–positron annihilation and other possible background events. This possibly provides a distinctive way to detect the radiation signatures for the production and oscillation of electron–positron pairs in ultra-strong electric fields that can be realized in either ground laboratories or astrophysical environments. (W.-B. Han, R. Ruffini, S.-S. Xue, Physics Letters B 691 (2010) 99). We focus our attention on studying how this oscillation frequency approaches the plasma frequency. The spectrum of this dipole radiation shows a unique line-like feature, as discussed above. The position of this feature, is determined as a function of the initial value of electric field strength. (A. Benedetti , W. B. Han, R. Ruffini, G.V. Vereshchagin, Physics Letters B6 98 (2011) 75). The ee⁻ pairs generated by the vacuum polarization process around a gravitationally collapsing charged core are entangled in the electromagnetic field (R. Ruffini, L. Vitagliano, S.-S. Xue, Phys. Lett. B 573, (2003) 33), and thermalize in an electron–positron–photon plasma on a time scale ~ 10⁴ t_C (R. Ruffini, L. Vitagliano, S.-S. Xue, Phys. Lett. B 559, (2003) 12). As soon as the thermalization has occurred, the hydrodynamic expansion of this electrically neutral plasma starts (R. Ruffini, J. Salmonson, J. Wilson, S.-S. Xue, A&A Vol. 335 (1999) 334; Vol. 359 (2000) 855). While the temporal evolution of the ee⁻ gravitationally collapsing core moves inwards, giving rise to a further amplified supercritical field, which in turn generates a larger amount of ee⁻ pairs leading to a yet higher temperature in the newly formed e⁺e⁻g plasma. We study this theoretically challenging process, which is marked by distinctive and precise quantum and general relativistic effects, and follow the dynamical phase of the formation of Dyadosphere and of the asymptotic approach to the horizon by examining the time varying process at the surface of the gravitationally collapsing core. We conclude that the core is not discharged or, in other words, the electric charge of the core is stable against vacuum polarization and electric field is amplified during the gravitational collapse. As a consequence, an enormous amount of pairs is left behind the collapsing core and Dyadosphere (G. Preparata, R. Ruffini, S.-S. Xue, A&A Vol. 338 (1998) L87) is formed. Recently, we study this pair-production process in a neutral collapsing stellar cores at or over nuclear densities，and show an overcritical electric field on the surface of baryon core. It is shown that in gravitational core-collapse, such an electric field dynamically evolves in the space-time and electron-positron pairs are produced, leading to the Dyadosphere of electron-positron pairs. This result has been published in (W. B. Han, R. Ruffini, S.-S. Xue, Physics Review D86,084004(2012). In order to understand the back-reaction of such electric energy building and radiating on collapse, we further adopt a simplified model describing the collapse of a spherically thin capacitor to give an analytical description how gravitational energy is converted to both kinetic and electric energies in collapse. It is shown that (i) averaged kinetic and electric energies are the same order, about an half of gravitational energy of spherically thin capacitor in collapse; (ii) caused by radiating and rebuilding electric energy, gravitational collapse undergoes a sequence of ``on and off'' hopping steps in the microscopic Compton scale. This has been published (R. Ruffini, and S-S. Xue , Physics Letters A377 (2013) 2450). Taking into account the Euler-Heisenberg effective Lagrangian of one-loop nonperturbative QED contributions, we formulate the Einstein-Euler-Heisenberg theory and study the solutions of nonrotating black holes with electric and magnetic charges in spherical geometry. In the limit of strong and weak electromagnetic fields of black holes, we calculate the black hole horizon radius, area, and total energy up to the leading order of QED corrections and discuss the black hole irreducible mass, entropy, and maximally extractable energy as well as the Christodoulou-Ruffini mass formula. This result has been published (R. Ruffini, Y.-B. Wu and S.-S. Xue, Physics Review D88, 085004 (2013)). An interesting aspect of effective field theories in the strong-field limit has recently been emphasized in a completely different class of quantum field theories. These have the property of developing in the strong-field limit an anomalous power behavior. We study and conclude that in the strong fields expansion, the leading order behavior of the Euler-Heisenberg effective Lagrangian is logarithmic, and can be formulated as a power law. These results have been published in (H. Kleinert, E. Strobel and S-S. Xue, Phys. Rev. D88, 025049 (2013)).

Particularly important is the report From nuclei to compact stars on page 1651. This activity has been carried out by a collaboration between D. Arnett, H. Kleinert, V. Popov, M. Rotondo, J. Rueda, R. Ruffini and S.-S. Xue. One of the most active field of research has been to analyze a general approach to Compact Stars like White-Dwarfs and Neutron Stars, based on the Thomas-Fermi ultrarelativistic equations amply adopted in the study of superheavy nuclei. The analysis of superheavy nuclei has historically represented a major field of research, developed by Prof. V. Popov and Prof. W. Greiner and their schools. In 2007 the ICRANet group found the welcome result that all the analytic work developed by Prof. V. Popov and the Russian school can be applied using scaling laws satisfied by the relativistic Thomas-Fermi equation to the case of nuclear matter cores of stellar dimensions, if the beta equilibrium condition is properly taken into account. Since then, a large variety of problems has emerged, which have seen the direct participation of the above mentioned ICRANet Faculty and Adjunct Faculty staff. In a set of seven appendixes, they have been presented the recent progresses made in the intervening years. First, the consideration made for an isolated core with constant proton density whose boundary has been sharply defined by a step function. No external forces are exerted. Then when the assumption of a sharp proton density profile has been relaxed and, consequently, a smooth surface modeled by a Woods-Saxon-like proton distribution has been introduced. The analysis of globally neutral and compressed configurations composed by a relativistic fluid of degenerate neutrons, protons, and electrons in beta equilibrium has been recently accomplished. It has been generalized the FeynmanMetropolis-Teller treatment of compressed atoms to relativistic regimes, and the concept of compressed nuclear matter cores of stellar dimensions has been introduced. Finally we studied the construction of neutron star configurations within a fully consistent formulation of the equations of equilibrium in general relativity and strong interactions, which has been covered in the Ph. D. thesis of D. Pugliese, R. Belvedere and S. Martins de Carvalho (see Fig. 21). This work has been successfully generalized to the case of uniformly rotating neutron stars, and it has been part of the Ph. D. thesis of R. Belvedere. The stability of neutron stars against mass-shedding and secular axisymmetric instabilities have been addressed. The analysis of the properties of the core-crust interface of a neutron star, such as its surface and Coulomb energies, and stability against perturbations have been studied by Y.~Wu and J. Pereira in their Ph. D. theses. This entire program has been developed in order to identify the initial boundary conditions for the electrodynamical process occurring at the onset of gravitational collapse leading to a black hole.

Figure 21: The core-crust transition in a fully general relativistic treatment of a neutron star considering strong, weak, electromagnetic and gravitational interactions

In parallel to this work on the neutron star, the introduction of the techniques for solving a compressed atom in a Wigner-Seitz cell has allowed to give a new approach to the study of degenerate matter in white dwarfs. This problem presents, still today, open issues of great interest such as the equilibrium of the electron gas and the associated nuclear component, taking into account the electromagnetic, the gravitational and the weak interactions formulated in a correct special and general relativistic framework. A complete analysis of the properties of such configurations as a function of the compression can be duly done through the relativistic generalization of the Feynman-Metropolis-Teller approach. It is then possible to derive a consistent equation of state for compressed matter which generalizes both the uniform free-electron fluid approximation, adopted for instance by Chandrasekhar in his famous treatment of white-dwarfs, and the well-known work of Salpeter which describes the electrodynamical and relativistic effects by a sequence of approximations. Apart from taking into account all possible electromagnetic and special relativistic corrections to the equation of state of white-dwarf matter, the new equation of state, which incorporates the beta equilibrium condition, leads to a self-consistent calculation of the onset for inverse beta-decay of a given nuclear composition as function of the Fermi energy of electrons or equivalently, as a function of the density of the system. This important achievement, leads to a self-consistent calculation of the critical mass of white-dwarfs with heavy nuclear composition. In addition, the numerical value of the mass, of the radius, and of the critical mass of white-dwarfs turn to be smaller with respect to the ones obtained with approximate equations of state. Therefore, the analysis of compressed atoms following the relativistic Feynman-Metropolis-Teller treatment has important consequences in the determination of the mass-radius relation of white dwarfs, leading to the possibility of a direct confrontation of these results with observations, in view of the current great interest for the cosmological implications of the type Ia supernovae. The generalization of the above Feynman-Metropolis-Teller treatment to the case of finite temperatures has been one of the subjects of the Ph. D. thesis of S. M. de Carvalho. The consequences of the thermal effects on the mass-radius relation of white dwarfs have been then scrutinized. The particular case of the low-mass white dwarfs that form binary systems with neutron stars, e.g. PSR J1738+0333, has been analyzed in detail. The equation of state obtained from the Feynman-Metropolis-Teller approach at finite temperatures has been tested in this low-mass (low-density) objects, where large from the zero temperature approximation are expected.

These two topics are leading to the preparation of a new book with Springer with the title “Von Kernen zu den Sternen” by J. Rueda and R. Ruffini.

The generalization of the general relativistic theory of white dwarfs to the rotating case has been successfully achieved in the thesis work of K. Boshkayev. The entire family of uniformly rotating stable white dwarfs has been already obtained by studying the mass-shedding, the inverse b-decay, pycnonuclear, and axisymmetric instabilities. The maximum mass and the minimum (maximum) rotation period (frequency) have been obtained for selected nuclear compositions. These results are relevant both for the theory of type Ia supernovae as well as for the recent work of M. Malheiro, J. Rueda and R. Ruffini on the description of Soft-Gamma-Ray Repeaters (SGRs) and Anomalous X-Ray Pulsars (AXPs) as rotation powered white dwarfs, following a pioneer idea of M. Morini et al. (1988) and of B. Paczynski (1990) on the AXP 1E 2259+586. The recent observation of SGR 0418+5729 promises to be an authentic Rosetta Stone, a powerful discriminant for alternative models of SGRs and AXPs. The loss of rotational energy of a neutron star cannot explain the X-ray luminosity of SGR 0418+5729, excluding the possibility of identifying this source as an ordinary spin-down powered neutron star. The inferred upper limit of the surface magnetic field of SGR 0418+5729 B < 7.5x10¹² G, describing it as a neutron star within the magnetic braking scenario, is well below the critical magnetic field B =2pmc³/(he) ~ 4.4x10¹³ Gauss, challenging the power mechanism based on magnetic field decay purported in the magnetar scenario. We have shown that the observed upper limit on the spin-down rate of SGR 0418+5729 is, instead, perfectly in line with a model based on a massive fast rotating highly magnetized white dwarf of fiducial mass M=1.4M_Sun, radius R=10³ km, and moment of inertia I ~ 10⁴⁹ g cm. We have analyzed the energetics of all SGRs and AXPs including their steady emission, the glitches and their subsequent outburst activities. It can be then shown that the occurrence of the glitch, the associated sudden shortening of the period, as well as the corresponding gain of rotational energy, can be explained by the release of gravitational energy associated to a sudden contraction and decrease of the moment of inertia of the white dwarfs, consistent with the conservation of their angular momentum. The energetics of the steady emission as well as the one of the outbursts following the glitch can be simply explained in term of the loss of the rotational energy in view of the moment of inertia of the white dwarfs, much larger than the one of neutron stars. There is no need here to invoke the decay of ultrastrong magnetic fields of the magnetar model (see Fig. 22). A more exhaustive analysis of SGR 0418+5729 within the white dwarf model has been recently achieved in the Ph. D. thesis of K. Boshkayev. The request of the rotational stability of the white dwarf gives bounds for the mass, radius, moment of inertia and magnetic field, through the analysis of constant rotation period sequences of uniformly rotating white dwarfs. We have also analyzed the emission properties in the optical band, and inferred the cyclotron frequencies associated to their magnetic fields which might cause absorption features in the optical wavelengths. The same analysis has been accomplished for Swift J1822.3-1606 and 1E 2259+586. We are in addition considering the possible progenitors of these massive fast rotating highly magnetized white dwarfs. We have considered the possibility that white dwarfs mergers could be the progenitor of white dwarfs with the above desirable properties, hence of SGRs and AXPs. In collaboration with P. Loren from University of Exeter in UK, and the group led by Prof. Garcia-Berro at Universitat Politecnica de Catalunya and Institute for Space Studies of Catalonia in Barcelona, we have performed numerical simulations of white dwarf mergers. We have shown that the products of these mergers consist of a hot central magnetized white dwarf surrounded by a heavy rapidly rotating disk. The evolution of the post-merger massive rapidly rotating magnetized white dwarf and its emission properties in the optical bands, have been computed. We have shown that these properties are consistent with AXPs such as 4U 0142+61, which show an infrared excess explainable via the existence of a dust disk, whereas the surface black body emission well describes the observations in the UV bands. The emission by these white dwarfs in the X-ray band is currently under consideration and it is the subject of the Ph. D. thesis of D. Cáceres.

Figure 22: Rotation period derivative versus the rotation period of SGRs and AXPs (red, blue and green). The dashed curves are contours of constant magnetic field, for a model based on white dwarfs.

The thermal evolution of neutron stars has been one of the thesis topics of S. M. de Carvalho. This work has been done in collaboration with R. Negreiros from Universidade Federal Fluminense in Brazil. The cooling curves of the novel neutron stars satisfying the condition of global charge neutrality have been obtained by full numerical integration of the radiative and transport equations in general relativity. A detailed comparison with the traditional case of locally neutral neutron stars has been performed.

The understanding of the theory of neutron stars has allowed the analysis of their role in astrophysical systems such as the GRBs, the GRB-Supernova, and the short GRBs. It has been analyzed in detail the binary progenitors of these systems with particular emphasis on the role played by neutron stars.

Concerning short GRBs, we had the first example that they are the result of the merger of neutron star binaries. F. Gomes Oliveira, as part of her Ph. D. thesis, has computed the evolution of binary neutron stars up to the merger point to evaluate the emission of gravitational waves in these systems. The dynamics has been simulated via the effective one-body formalism of Prof. Thibault Damour, up to fourth post-Newtonian order. The detectability of this emission by second generation detectors such as Advanced LIGO has been assessed, and the total energy output in gravitational waves has been compared with the observed emission in both X and gamma rays. This work has been possible thanks to the analysis of the first genuinely short GRB, GRB 090227B by Muccino et al. (2013), where it has been shown that the properties of this GRB indeed are consistent with a binary neutron star progenitor.

There are other aspects of GRBs where the physics of neutron stars plays an important role and where the different aspects of a detailed description of the neutron star interior described above acquire a specific value. This is the case of the process of induced gravitational collapse of a neutron star to a black hole by a supernova in a binary system. I come back to this point later on, to the distinction between long and short GRBs, as well as the GRB-SN connection.

The topic about Symmetries in General Relativity (the full report is on page 2193) has been developed as an intense collaboration between various research groups. Profs. R.T. Jantzen, L. Stella (Observatory of Monte Porzio, Rome), O. Semerak (Czech Republic), D. Bini and Dr. A. Geralico have studied the problem of motion of test particles in black hole spacetimes, in presence of a superposed radiation field. The scattering of radiation by the test particles causes a friction-like drag force which forces particles on certain equilibrium orbits outside the black hole horizon. This interesting effect, known as Poynting-Robertson effect, has been deeply investigated in many different contexts: besides the Schwarzschild and Kerr black hole, novel results have been published for the case of a Vaidya radiation metric. In the latter case, in fact, one takes the advantages of having an exact solution of the Einstein’s field equations whose source is a null field. Among the various consequences we mention that while a unique equilibrium circular orbit exists if the photon flux has zero angular momentum, multiple such orbits appear if the photon angular momentum is sufficiently high. Furthermore other solutions of the Weyl class with cylindrical symmetry as well as solutions within the class of exact gravitational plane waves and electromagnetic plane waves have been examined in the context of Poynting-Robertson like effects obtaining a number of physically relevant situations. Bini and Geralico have also considered the motion of spinning test particles in Kerr spacetime in full generality with the aim to study deviations between the world lines of spinning objects in comparison with those of geodesic test particles, generalizing some recent works on the same topic where motion were but constrained on the equatorial plane. Bini, Geralico and Jantzen have been able to obtain new foliations in spacetimes admitting separable geodesics. These “separable geodesic action slicing” have been used then to explore certain geometrical properties of horizon penetrating coordinates in black hole spacetimes. Other collaborations, again for what concerns the topics included in symmetries in General Relativity, have been started with Profs. A. Ortolan (INFN Legnaro, Padova, Italy) and P. Fortini (University of Ferrara, Italy) to study of the interaction of electromagnetic waves with gravitational waves, with the gravitational waves considered in the exact theory and not in its linear approximation.

In collaboration with Campus Bio-Medico in Rome there are ongoing researches on galactic structures. The Reports “Self Gravitating Systems, Galactic Structures and Galactic Dynamics” on page 2305 is focused on analytical and numerical methods for the study of classical self-gravitating fluid/gaseous masses. A series of papers of this group have been devoted in the past to the generalization of the classical theory of ellipsoidal figures of equilibrium using virial methods. The research activities of the group have focused subsequently on functional methods for obtaining equilibrium solutions for polytropic self-gravitating systems that rotate and have a non uniform vorticity. The group has recently published a novel and important result in the context of analogous geometry theory. It is well known that the wave equation for the perturbations of given a perfect barotropic and irrotational Newtonian fluid can be rewritten as an “effective General Relativity”. They have extended this result including the possibility for the fluid to be self-gravitating. This work opens the path for a new interpretation of classical white-dwarf theory in terms of curved space-time techniques. The group has also studied the perturbations of classical compressible rotating but not gravitating fluids as occurring in generalized acoustic black holes. It has also analyzed the Analog Gravity formalism at full nonlinear level through Von Mises’ Wave Equation for irrotational configurations.

We recall the successful attempt of applying methodologies developed in Relativistic Astrophysics and Theoretical Physics to researches in the medicine domain. The Report “Interdisciplinary Complex Systems” on page 2335 adopts analytical and numerical methods for the study of problems of nonlinear dynamics focusing on biological systems and using a theoretical physics approach. It is well established both numerically and experimentally that nonlinear systems involving diffusion, chemotaxis, and/or convection mechanisms can generate complicated time-dependent spiral waves, as in happens in chemical reactions, slime molds, brain and in the heart. Because this phenomenon is global in Nature and arises also in astrophysics with spiral galaxies, the goal of this research activity has been to clarify the role of this universal spiraling pattern. The group has studied numerically the nonlinear partial differential equations of the theory (Reaction-Diffusion) using finite element methods. The group has recently published moreover a novel and important result: an electromechanical model of cardiac tissue, on which spiral moves and causes the domain to deform in space and time (see Fig. 23). This model is a real breakthrough in the context of theoretical biophysics, leading to new scenarios in the context of computational cardiology. In 2011 the group has focused its research on classical hydrodynamics, evaluating the stress exerted by the fluid on the domain walls and introducing an indicator of risk for their damage. Such a methodology, named as “three-band decomposition analysis of wall shear stress in pulsatile flows”, has been immediately applied to hemodynamical problems which have been numerically integrated (see Fig. 24), but results promising also for other problems of physical and biological sciences and for engineering.

Figure 23: Electrical activity map of an electro-elastic deformed patch of cardiac-type tissue

Figure 24: Turbulent flow structure (specifically the velocity amplitude) in a deformed vessel, obtained by numerical integration through finite elements of the incompressible Navier-Stokes equations.

The next contribution is the one by Jaan Einasto of the Tartu Astronomical Observatory. Prof. Einasto has been collaborating in the previous year intensively within ICRA about the large scale structure of the Universe and its possible fractal structure. With Prof. Einasto there is also the collaboration of Prof. G. Hutsi. Since two years Prof. Einasto is an Adjunct Professor of ICRANet and an active member of the Faculty of the IRAP PhD. In this role Prof. Einasto has delivered a set of lectures in the months of February and September 2010 on “The large scale structure of the universe: a powerful probe for fundamental physics”. This topic was covered with a quantitative analysis of the distribution of galaxies, on dark matter, on the cosmological parameters and dark energy. At the moment, Prof. Einasto has completed a book reviewing the status of the dark matter and the large scale structure of the universe published by World Scientific as Volume 14^th in the Advanced Series in Astrophysics and Cosmology Series edited by L.Z. Fang and R. Ruffini. This book covers the material of the lectures delivered in the IRAP PhD program as well as an historical perspective between the different approaches to the study of the dark matter content of the universe in the west and in the former Soviet union. The full report is on page 1177.

An important fundamental research topic is the investigation of “analogue models of gravity”. Such models have been used to understand many aspect of gravitational phenomena, in particular the mechanism of Hawking-and Unruh-Radiation, by studying in supersonic flow nozzles. These were of great help in dispersing criticism of these radiations based on our ignorance of the divergences of local quantum field theory at ultrashort distances. Another important analogy is bases on the relation between Einstein-Cartan Physics and the theory of defects in solids, worked out in detail in the textbook by our adjunct faculty members H. Kleinert: < http://users.physik.fu berlin.de/~kleinert/kleinert/?p=booklist&details=1 >. This analogy has recently allowed to understand the equivalence of Einstein's theory of gravitation with his Teleparallel Theory of Gravitation as a result of a novel gauge symmetry. The first uses only the curvature of spacetime to explain gravitational forces, while the second uses only torsion. The equivalence relies on the fact that crystalline defects of rotation and translation (disclinations and dislocations, respectively) are not independent of each other, but the ones can be understood as superpositions of the other. Moreover, the analogy has allowed to set up an infinite family of intermediate theories in which curvature and torsion appear both < http://klnrt.de/385/385.pdf >. Finally, all geometries relevant in gravitational physics has been derived from a completely new theory of multivalued fields < http://www.physik.fu-berlin.de/~kleinert/kleinert/?p=booklist&details=9 >.