Stability Analysis in N dimensional Gravitational collapse with equation of state
| Autor: | Sarwe, Sanjay, Saraykar, R. V. |
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| Rok vydání: | 2012 |
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| Zdroj: | Grav.Cosmol. 20(2014) 282-289 |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $p = k \rho$, $0 \leq k \leq 1$. We prove that for a regular initial data comprising of pressure (or density) profiles at an initial surface $t = t_{i}$, 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. Comment: 11 pages. arXiv admin note: text overlap with arXiv:gr-qc/0406052 by other authors |
| Databáze: | arXiv |
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