On evolution of the pair-electromagnetic pulse of a charged black hole

Abstract

Abstract. 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, electronpositron 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, observationsIn 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 e + e − pair production. In Reissner-Nordstrom EMBHs, the horizon radius is expressed asThe outer limit of the dyadosphere is defined as the radius r ds at which the electric field of the EMBH equals this critical fieldThe total energy of pairs, converted from the static electric energy, deposited within a dyadosphere is thenIn Wilson (1975Wilson ( , 1977 a black hole charge of the order 10% was formed. Thus, we henceforth assume a black hole charge Q = 0.1Q max , Q max = √ GM for our detailed numerical calculations. The range of energy is of interest as a possible gamma-ray burst source. In order to model the radially resolved evolution of the energy deposited within the e + e − -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 iswhereWe assume the plasma fluid of e + e − -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)where ρ and p are respectively the total proper energy density and pressure in the comoving frame. The U µ is the four-velocity of the plasma fluid. The baryon-number and energy-momentum conservation laws arewhere n B is the baryon-number density. The radial component of Eq. (7) reduces to ∂p ∂rThe component of the energy-momentum conservation Eq. (7) Equations (6) and (9) give rise to the relativistic hydrodynamic equations.

On the Structure of the Burst and Afterglow of Gamma-Ray Bursts I: The Radial Approximation

“…After the discovery of the afterglow of GRBs and the determination of the cosmological distance of their sources we noticed the coincidence between the theoretically predicted energetics and the observed ones in Damour & Ruffini (1975 ): 47 we returned to our theoretical results developing some new basic theoretical concepts, 46,69,48,49,50 which have led to the EMBH theory.…”

“…The Livermore code 49 has shown very clearly the self organization of the expanding plasma in a very sharp pulse which we have defined as the pair-electromagnetic pulse (PEM pulse), in analogy with the EM pulse observed in nuclear explosions. In order to further examine the structure of the PEM pulse with the simpler procedures of the Rome codes we have assumed 49 three alternative patterns of expansion of the PEM pulse on which to try the simplified special relativistic treatment and then compared the results with the fully general relativistic hydrodynamical results:…”

“…(53,54,56) (obtained at Livermore). 49 Details of the iterative method used to solve the special relativistic equation can be found in Ruffini, Salmonson, Wilson & Xue (1999).…”

What can we learn from GRBs?

“…Its expansion and self-acceleration is due to the gradual e + e − annihilation [59]. Even after engulfing the baryonic mass M B left over by the progenitor system, quantified by the baryon load B = M B c 2 /E tot e + e − [60], the fireshell remains still optically thick and continues its self-acceleration up to ultrarelativistic velocities [61,62]. When the fireshell reaches the transparency condition, a first flash of radiation, the P-GRB, is emitted [7,59,60].…”

“…Even after engulfing the baryonic mass M B left over by the progenitor system, quantified by the baryon load B = M B c 2 /E tot e + e − [60], the fireshell remains still optically thick and continues its self-acceleration up to ultrarelativistic velocities [61,62]. When the fireshell reaches the transparency condition, a first flash of radiation, the P-GRB, is emitted [7,59,60]. The spectrum of the P-GRB is determined by the geometry of the pair-creation region: in the case of the spherically symmetric dyadosphere, the P-GRB spectrum is generally described by a single thermal component [42].…”