Relativity and Cosmology


The Chronology Protection Conjecture and the Formation of the Kerr Black Hole Through Gravitational Collapse

Authors: Moninder Singh Modgil

Exterior of the Kerr black hole is considered as the likely spacetime geometry around a black hole formed by gravitational collapse. However the Kerr black hole has chronology violating Closed Time-like Curves (CTCs), near the ring singularity in interior. Hawking has considered formation of CTCs using a scalar field and shown that back reaction of nature - divergence of energy-momentum tensor - would prevent formation of CTCs. The question being raised here is whether the physics behind Hawking's concept of "chronology protection", will actually prevent formation of the Kerr black hole - through gravitational collapse. On the other hand, if the Kerr black hole indeed gets formed by gravitational collapse, then one has a counter example to Chronology Protection Conjecture. Chronology protection thus imposes the constraint that formation of a rotating black hole through gravitational collapse should be such that the interior metric of the black hole does not match that of the Kerr black hole, or any other black hole with CTCs. It is possible that the quantum gravity effects rule out formation of CTCs during gravitational collapse - as they are expected to remove singularities. There may however be classical solutions to the problem. Angular momentum orginating from the rotation and the formation of CTCs are intimately related - through the off diagonal term $g_{t \phi}$ i.e., the coefficient of the $dtd\phi$ term (corresponding to the temporal coordinate $t$ and the longitudinal angular coordinate $\phi$) - of the metric tensor. A possible solution is that during the gravitational collapse, all the angular momentum of the star, is radiated away by gravitational waves - leaving behind as residual, the Schwarzschild black hole.

Comments: 6 Pages.

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[v1] 2018-07-20 03:25:22

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