Critical Collapse of an Ultrarelativistic Fluid in the $Γ\to 1$ Limit

Martin Snajdr

doi:10.1088/0264-9381/23/10/006

paper

Critical Collapse of an Ultrarelativistic Fluid in the $Γ \to 1$ Limit

arXiv:gr-qc/0508062 · doi:10.1088/0264-9381/23/10/006

Abstract

In this paper we investigate the critical collapse of an ultrarelativistic perfect fluid with the equation of state $P = (Γ - 1) ρ$ in the limit of $Γ \to 1$ . We calculate the limiting continuously self similar (CSS) solution and the limiting scaling exponent by exploiting self-similarity of the solution. We also solve the complete set of equations governing the gravitational collapse numerically for $(Γ - 1) = 1 0^{- 2}, ..., 1 0^{- 6}$ and compare them with the CSS solutions. We also investigate the supercritical regime and discuss the hypothesis of naked singularity formation in a generic gravitational collapse. The numerical calculations make use of advanced methods such as high resolution shock capturing evolution scheme for the matter evolution, adaptive mesh refinement, and quadruple precision arithmetic. The treatment of vacuum is also non standard. We were able to tune the critical parameter up to 30 significant digits and to calculate the scaling exponents accurately. The numerical results agree very well with those calculated using the CSS ansatz. The analysis of the collapse in the supercritical regime supports the hypothesis of the existence of naked singularities formed during a generic gravitational collapse.

23 pages, 16 figures, revised version, added new results of investigation of a supercritical collapse and the existence of naked singularities in generic gravitational collapse

References in corpus (1)

Assessment of a high-resolution central scheme for the solution of the relativistic hydrodynamics equations

Critical Collapse of an Ultrarelativistic Fluid in the Γ→1 Limit

Abstract

References in corpus (1)

Cited by in corpus (6)

Critical Collapse of an Ultrarelativistic Fluid in the $Γ \to 1$ Limit