2012/11/30 by Sanjay Sarwe, R. V. Saraykar
Physics and Astronomy · #gr-qc
published as Grav.Cosmol. 20(2014) 282-289 · 11 pages. arXiv admin note: text overlap with arXiv:gr-qc/0406052 by other authors
arxiv created 2014/11/25 · arxiv updated 2014/11/26
We study stability of occurrence of black holes and naked singularities that arise as a final state for a complete gravitational collapse of type I matter field in a spherically symmetric N dimensional spacetime with equation of state p = k ρ, 0 ≤ k ≤ 1. We prove that for a regular initial data comprising of pressure (or density) profiles at an initial surface t = ti, from which the collapse evolves, there exists a large class of the velocity functions and classes of solutions of Einstein equations, such that the spacetime evolution goes to a final state which is either a black hole or a naked singularity. We further prove that in an infinite dimensional separable Banach space, the set of regular initial data leading the collapse to a black hole or a naked singularity, forms an open subset of the set of all regular initial data. In this sense, the gravitational collapse leading to either a black hole or a naked singularity is stable. These results are discussed and analyzed in the light of the cosmic censorship hypothesis in black hole physics.