On the Relation Between Quasi-Normal Modes and Circular Null Geodesics

Gollapudi, Praveer Krishna (2019) On the Relation Between Quasi-Normal Modes and Circular Null Geodesics. Masters thesis, Indian Institute of Science Education and Research Kolkata.

PDF (MR dissertation of Praveer Krishna Gollapudi (17MR002)) 17MR002.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

The 2016 announcement by the LIGO consortium of the detection of gravitational waves(GW) from a pair of merging black holes marked the inception of gravitational wave astronomy. As seen in this new medium, the Universe can be probed to a greater degree than was ever possible by electromagnetic(EM) means. One can not only corroborate events glimpsed in the EM spectrum, but also observe those beyond the reach of EM waves- from the implosion of distant stars to the inflation of the early Universe. One very important phenomenon that GW allow us to observe is the characteristic oscillation of black holes, called quasi-normal modes(QNM). Just as stars are known to oscillate in certain modes, so too are black holes known to give off gravitational radiation when perturbed. And similar to how EM observations of stellar oscillations can provide insights into the structure and stability of stars, observations of QNM can provide critical information regarding the structure of the objects that we encounter in GW astronomy. Like any other sub-field of general relativity, black hole perturbation is rich in examples and applications. In the present work, we examine the particularly intriguing relation that seems to exist between the quasi-normal frequencies of a black hole, and its equatorial null geodesics. We shall present the basis of existing claims, comment on a few counter-claims, and finally wrap up by investigating the presence of this relation in a new case.

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