Abstract:
We recall the generalization of the Feynman-Metropolis-Teller approximation for a compressed atom using a relativistic Fermi-Thomas model. These results within a Wigner-Seitz approximation lead to a new equation of state for white dwarfs and to a new value of their critical mass, smaller than the one obtained by Chandrasekhar. The possible observations of these effects in binary neutron stars are outlined.

Abstract:
The idea that the vacuum polarization process occurring during gravitational collapse to a black hole endowed with electromagnetic structure (EMBH) could be the origin of gamma ray bursts (GRBs) is further developed. EMBHs in the range 3.2 -- 10$^6$ solar masses are considered. The formation of such an EMBH, the extraction of its mass-energy by reversible transformations and the expansion of the pair-electromagnetic pulse (PEM pulse) are all examined within general relativity. The PEM pulse is shown to accelerate particles to speeds with Lorentz gamma factors way beyond any existing experiment on Earth. Details of the expected burst structures and other observable properties are examined.

Abstract:
Patterns in the scientific developments of Relativistic Astrophysics are analyzed with special attention to the physics and astrophysics of Black Holes and Gamma Ray Bursts.

Abstract:
The developments of the elctromgnetic black holes physics and vacuum polarization process are presented in the interpretation of Gamma-Ray Bursts.

Abstract:
A new version of the Teukolksy Master Equation, describing any massless field of different spin $s=1/2,1,3/2,2$ in the Kerr black hole, is presented here in the form of a wave equation containing additional curvature terms. These results suggest a relation between curvature perturbation theory in general relativity and the exact wave equations satisfied by the Weyl and the Maxwell tensors, known in the literature as the de Rham-Lichnerowicz Laplacian equations. We discuss these Laplacians both in the Newman-Penrose formalism and in the Geroch-Held-Penrose variant for an arbitrary vacuum spacetime. Perturbative expansion of these wave equations results in a recursive scheme valid for higher orders. This approach, apart from the obvious implications for the gravitational and electromagnetic wave propagation on a curved spacetime, explains and extends the results in the literature for perturbative analysis by clarifying their true origins in the exact theory.

Abstract:
We review recent progress in our understanding of the nature of gamma ray bursts (GRBs) and in particular, of the relationship between short GRBs and long GRBs. The first example of a short GRB is described. The coincidental occurrence of a GRB with a supernova (SN) is explained within the induced gravitational collapse (IGC) paradigm, following the sequence: 1) an initial binary system consists of a compact carbon-oxygen (CO) core star and a neutron star (NS); 2) the CO core explodes as a SN, and part of the SN ejecta accretes onto the NS which reaches its critical mass and collapses to a black hole (BH) giving rise to a GRB; 3) a new NS is generated by the SN as a remnant. The observational consequences of this scenario are outlined.

Abstract:
Gamma-ray bursts (GRBs) and supernovae (SNe) bring new perspectives to the study of neutron stars and white dwarfs, as well as opening new branches of theoretical physics and astrophysics.

Abstract:
Recent work on the dyadosphere of a black hole is reviewed with special emphasis on the explanation of gamma ray bursts. A change of paradigm in the observations of black holes is presented.

Abstract:
The "dyadosphere" (from the Greek word "duas-duados" for pairs) is here defined as the region outside the horizon of a black hole endowed with an electromagnetic field (abbreviated to EMBH for "electromagnetic black hole") where the electromagnetic field exceeds the critical value, predicted by Heisenberg and Euler for electron-positron pair production. In a very short time, a very large number of pairs is created there. I give limits on the EMBH parameters leading to a Dyadosphere for 10 solar mass and 100000 solar mass EMBH's, and give as well the pair densities as functions of the radial coordinate. These data give the initial conditions for the analysis of an enormous pair-electromagnetic-pulse or "PEM-pulse" which naturally leads to relativistic expansion. Basic energy requirements for gamma ray bursts (GRB), including GRB971214 recently observed at z=3.4, can be accounted for by processes occurring in the dyadosphere.