*Astron. Astrophys. Suppl. Ser.* **138**, 513-514

**R. Ruffini**

I.C.R.A.-International Center for Relativistic Astrophysics and
Physics Department, University of Rome "La Sapienza", I-00185 Rome,
Italy

e-mail: ruffini@icra.it

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 E 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 _{1}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:

- They occur in an extended region arround the Black Hole, the Dyadosphere,
extending from the horizon radius
*r*to the Dyadosphere radius see (Preparata et al. 1998a,b). Only Black Holes with a mass larger than the upper limit of a neutron star and up to a maximum mass of can have a Dyadosphere, see (Preparata et al. 1998a,b) for details._{+} - The efficiency of transforming the mass-energy of Black Hole into particle-antiparticle pairs outside the horizon can approach 100%, for Black Holes in the above mass range see (Preparata et al. 1998a,b) for details.
- The pair created are mainly positron-electron pairs and their number is much
larger than the quantity
*Q*/*e*one would have naively expected on the ground of qualitative considerations. It is actually given by , where*m*is the electron mass. The energy of the pairs and consequently the emission of the associated electromagnetic radiation peaks in the X-gamma rays region, as a function of the Black Hole mass.

(1) |

(2) |

(3) |

(4) |

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

(5) |

Copyright The European Southern Observatory (ESO)