*Astron. Astrophys. Suppl. Ser.* **138**, 511-512

**R. Ruffini ^{1} -
J.D. Salmonson^{2} -
J.R. Wilson^{2} -
S.-S. Xue^{1}
**

1 -
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

2 -
Lawrence Livemore National Laboratory, University of
California, Livermore, California, U.S.A.

Received January 21; accepted March 10, 1999

Using hydrodynamic computer codes, we study the possible patterns of relativistic expansion of an enormous pair-electromagnetic-pulse (P.E.M. pulse); a hot, high density plasma composed of photons, electron-positron pairs and baryons deposited near a charged black hole (EMBH). On the bases of baryon-loading and energy conservation, we study the bulk Lorentz factor of expansion of the P.E.M. pulse by both numerical and analytical methods.

**Key words: **black hole physics -- gamma-ray bursts,
theory, observations

In the paper by
Preparata et al. (1998),
the "dyadosphere" is defined as the
region outside the horizon of a
EMBH where the electric field exceeds the critical value for pair production. In Reissner-Nordstrom EMBHs, the horizon
radius is expressed as

(1) |

(2) |

(3) |

In order to model the radially resolved evolution of the energy deposited within the -pair and photon plasma fluid created in the dyadosphere of EMBH, we need to discuss the relativistic hydrodynamic equations describing such evolution.

The metric for a Reissner-Nordstrom black hole is

(4) |

We assume the plasma fluid of -pairs, photons and baryons to be a simple perfect fluid in the curved spacetime (Eq. (4)). The stress-energy tensor describing such a fluid is given by (Misner et al. 1975)

(5) |

(6) | ||

(7) |

(8) |

(9) |

We now turn to the analysis of pairs initially created in
the Dyadosphere. Let be the proper densities of
electrons and positrons ().
The rate equation for is

(10) |

(11) |

(12) |

(13) |

We use a computer code
(Wilson et al. 1997, 1998)
to evolve the spherically symmetric hydrodynamic equations for the
baryons, -pairs and photons deposited in the Dyadosphere. In
addition, we use an analytical model to integrate the spherically
symmetric hydrodynamic equations with the following geometries of
plasma fluid expansion: (i) spherical model: the radial component of
four-velocity , where *U* is four-velocity at
the surface () of the plasma, (ii) slab 1: , the constant width of expanding slab in
the coordinate frame of the plasma; (iii) slab 2: the constant width
of expanding slab in the comoving frame of the
plasma.

We compute the relativistic Lorentz factor of the expanding pair and photon plasma. We compare these hydrodynamic calculations with simple models of the expansion. In Fig. 1 we see a comparison of the Lorentz factor of the expanding fluid as a function of radius for all of the models. We can see that the one-dimensional code (only a few significant points are pesented) matches the expansion pattern of a shell of constant coordinate thickness (slab 1).

We have shown that a relativistically expanding P.E.M. pulse can
originate from the Dyadosphere of a EMBH. The P.E.M. pulse can produce
gamma-ray bursts having the general characteristics of observed
bursts. For example, the burst energy for a BH is 3
10^{54} ergs with a spectral peak at 500 keV and a pulse
duration of 40 seconds
(Ruffini et al. 1999).
This oversimplified model is encouraging enough to demand further
study of the Dyadosphere created by EMBHs.

Copyright The European Southern Observatory (ESO)