ar X iv : g r - qc / 0 50 80 62 v 1 1 6 A ug 2 00 5 Critical Collapse of an Ultrarelativistic Fluid in the Γ → 1 Limit

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 → 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) = 10, . . . , 10 and compare them with the CSS solutions. 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. PACS numbers: 04.20.Dw,04.25.Dm,04.40.Nr,04.70.Bw,02.60.-x,02.60.Cb