Gravitational collapse of a Hagedorn fluid in Vaidya geometry

Abstract

The gravitational collapse of a high-density null charged matter fluid, satisfying the Hagedorn equation of state, is considered in the framework of the Vaidya geometry. The general solution of the gravitational field equations can be obtained in an exact parametric form. The conditions for the formation of a naked singularity, as a result of the collapse of the compact object, are also investigated. For an appropriate choice of the arbitrary integration functions the null radial outgoing geodesic, originating from the shell focussing central singularity, admits one or more positive roots. Hence a collapsing Hagedorn fluid could end either as a black hole, or as a naked singularity. A possible astrophysical application of the model, to describe the energy source of gamma-ray bursts, is also considered.

Null fluid collapse in brane world models

“…as in [184] and again assuming the limit given in Eq. (106), the singularity is locally naked if the equation…”

“…In contrast, short GRBs are usually found to originate from nearby early-type galaxies, with little star formation, which is in good agreement with the conjecture that they originate from mergers of compact binaries. However, this simple paradigm is challenged by a few unusual GRBs, so that more exotic models, such as energy emission from superconducting cosmic strings [227][228][229], or from the collapse of ultra-high density stars described by a Hagedorn fluid [184], may be viable progenitors for explaining anomalous results.…”

“…The method of analysis follows that presented in [184], but is applied instead to the solutions of the brane world field equations obtained in the ρ(u, r) → ∞ limit, rather than to the general-relativistic solution. For comparison to the data, we again choose the GRB observations, GRB 971214 and GRB 990123, with isotropic energy losses of order 10 53 and 10 54 erg, respectively [230], and explicitly include factors of c in our analysis.…”

“…In [184], the gravitational collapse of Hagedorn matter in the Vaidya geometry, ending in a naked singularity, was investigated as a possible source of gamma-ray bursts (GRBs). GRBs are cosmic gamma-ray emissions with typical fluxes of the order 10 −5 to 5×10 −4 erg cm −2 and durations from 10 −2 to 10 3 s [197].…”

“…If one considers an ensemble of weekly interacting strings at a finite temperature, the behavior of the density of states is thought to lead either to a limiting temperature, or to a phase transition in which the string configuration changes to one which is dominated by a single long string [179]. The high density Hagedorn phase of matter has also been extensively used in cosmology to describe the very early phases of the evolution of the Universe [180][181][182][183] and the spherically-symmetric collapse of a Hagedorn fluid in the Vaidya geometry has been studied in [184].…”