Possibility of Over-spinning Kerr Blackhole

Malakar, Dishari (2021) Possibility of Over-spinning Kerr Blackhole. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Dishari Malakar (16MS125)) 16MS125_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (2MB)

Abstract

The project has been divided into two parts: “Carter constant" and “Over-spinning of Kerr blackholes." Carter constant is a non-trivial constant of motion that is a manifestation of hidden symmetries in the stationary axisymmetric spacetime, eg. the Kerr blackhole. Carter proposed the idea of finding the constant through the inspection of the Hamiltonian, called the “Carter theorem". We applied the formulation of finding non-trivial constants of motion for a metric whose Hamiltonian is of the form of Carter separability. But, due to the complicated generalized structure of the metric, it was not possible to get a physical picture of the spacetime by solving the Einstein’s vacuum equations. Jacobson had shown that it is possible to over-spin a nearly extremal Kerr blackhole using a test particle. Over-spinning is nothing but the violation of cosmic censorship conjecture by making the angular momentum parameter a greater than the mass M, in case of a Kerr blackhole. Extending Jacobson’s work, we assumed a ray of timelike particles following equatorial geodesics are projected towards the Kerr blackhole from infinity. The particles deposit mass and angular momentum to the blackhole and increases the same for the blackhole. The mass and angular momentum of the blackhole are calculated by projecting the stress-energy tensor in the direction of horizon generating Killing vector and spacelike Killing vector respectively, followed by integrating them over the event horizon hypersurface. We evaluate the recursion relation for the mass and angular momentum a and plot them against n. The methodology has been done in both Kerr-Schild and Boyer-Lindquist coordinates. We have shown that overspinning is not possible considering our assumptions. Only for the case of extremal blackholes, it was possible to violate the cosmic censorship by 1 particle if M =a<1/4 (in Kerr-Schild) and M =a<1/2 (in Boyer-Lindquist). We have also extended our problem to null equatorial geodesics and obtained similar results.

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