Astron. Astrophys. Suppl. Ser. 138, 513-514
I.C.R.A.-International Center for Relativistic Astrophysics and
Physics Department, University of Rome "La Sapienza", I-00185 Rome,
Received January 21; accepted March 12, 1999
Works on the Dyadosphere are reviewed.
Key words: black holes physics -- gamma-rays: bursts
I am proposing and give reasons that with Gamma Ray Bursts, for the first time we are witnessing, in real time, the moment of gravitational collapse to a Black Hole. Even more important, the tremendous energies involved by the energetics of these sources, especially after the discoveries of their afterglows and their cosmological distances (Kulkarni et al. 1998), clearly point to the necessity and give the opportunity to use as an energy source of these objects the extractable energy of Black Holes.
That Black Holes can only be characterized by their mass-energy E, charge Q and angular momentum L has been advanced in a classical article (Ruffini & Wheeler 1971), the proof of this has been made after twenty five years of meticulous mathematical work. One of the crucial points in the Physics of Black Holes was to realize that energies comparable to their total mass-energy could be extracted from them. The computation of the first specific example of such an energy extraction process, by a experiment Gedanken, was given in (Ruffini & Wheeler 1970) and (Floyd & Penrose 1971) for the rotational energy extraction from a Kerr Black hole, see Fig. 1. The reason of showing this figure is not only to recall the first such explicit computation, but to emphasize how contrived and difficult such a mechanism can be: it can only work for very special parameters and should be in general associated to a reduction of the rest mass of the particle involved in the process. To slow down the rotation of a Black Hole and to increase its horizon by the accretion of counterrotating particles is almost trivial, but to extract the rotational energy from a Black Hole, namely to slow down the Black Hole and keep its surface area constant, is extremely difficult, as clearly pointed out also by the example in Fig. 1. The above experiment Gedanken, extended as well to electromagnetic interactions, became of paramount importance not for their direct astrophysical significance but because they gave the tool for testing the physics of Black Holes and identifing their general mass-energy formula (Christodoulou & Ruffini 1971). The crucial point is that a transformation at constant surface area of the Black Hole, or reversible in the sense of reference Christodoulou & Ruffini (1971), could release an energy up to 29% of the mass-energy of an extremal rotating Black Hole and up to 50% of the mass-energy of an extremely magnetized and charged Black Hole.
|Figure: (Reproduced from Ruffini and Wheeler with their kind permission.) Decay of a particle of rest-plus-kinetic energy into a particle which is captured into the black hole with positive energy as judged locally, but negative energy E1 as judged from infinity, together with a particle of rest-plus-kinetic energy which escapes to infinity. The cross-hatched curves give the effective potential (gravitational plus centrifugal) defined by the solution E of Eq. (2) for constant values of and (figure and caption reproduced from Christodoulou 1970)|
Various models have been proposed in order to tap the rotational energy of Black Holes by the processes of relativistic magnetohydrodynamic. It is likely however that these processes are relevant over the very long time scales characteristic of the accretion processes.
In the present case of the Gamma Ray Bursts a prompt mechanism, on time scales shorter than a second, for depositing the entire energy in the fireball at the moment of the triggering process of the burst, appears to be at work. For this reason we are here considering a more detailed study of the vacuum polarization processes à a'la Heisenberg-Euler-Schwinger (Heisenberg & Euler 1931; Schwinger 1951) around a Kerr-Newman Black Hole first introduced by Damour and Ruffini (Damour & Ruffini 1975). The fundamental points of this process can be simply summarized:
Before concluding I would like to return to the suggestion, advanced by Damour and
Ruffini, that a discharged EMBH can be still extremely interesting from an energetic
point of view and responsible for the acceleration of ultrahigh energy cosmic rays. I
would like just to formalize this point with a few equations: It is clear that no
matter what the initial conditions leading to the formation of the EMBH are, the final
outcome after the tremendous expulsion of the PEM pulse will be precisely a Kerr
Newman solution with a critical value of the charge. If the background metric has a
killing vector, the scalar product of the killing vector and the generalized momentum
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