Linear isentropic Equation of State in formation of Black hole and Naked singularity

Sarwe S.

Department of Mathematics, S. F. S. College, Seminary Hill, Nagpur, India

E-mail: Sarwe sbsarwe@gmail.com

We analyze the physical process of gravitational collapse of a spherically symmetric perfect fluid space-time with a linear isentropic equation of state p = kρ. We propose two models, with ansatzes (i) v׳ (t,r)/v(t,r) = ξ'(r) and ( ii ) rv׳(t,r)/v(t,r) = g(v) that give rise to a family of solutions to Einstein equations with equation of state that evolves from a regular initial data satisfying weak energy conditions. The model with first ansatz leads to homogeneous collapse that terminates into the formation of black hole. We establish that as the parameter k → 1 in the range −1/3 < k ≤ 1, the formation of black hole gets accelerated in time, revealing the significance of equation of state in black hole formation.

In the second model, the end state of collapse in marginally bound spacetime is investigated in the range 0 < k ≤ 1. It is shown that end state of the inhomogeneous collapse culminates into formation of black hole and naked singularity, and that solely depends on the generic regular initial data and the role played by the pressure through parameter k. These studies give us deeper insights into the final states of collapse with a physically relevant equation of state in the light of cosmic censorship conjecture.

Keywords: Gravitational Collapse, Equation of state, Black holes and Naked singularities.

DOI: 10.18698/2309-7604-2015-1-454-467

Article file: Sarwe.pdf