Rigidity of marginally outer trapped surfaces in Reissner-Nordström spacetime

Akhter, Sharmin (2021) Rigidity of marginally outer trapped surfaces in Reissner-Nordström spacetime. Masters thesis, Memorial University of Newfoundland.

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Abstract

Our primary focus in this thesis is to investigate the stability vs rigidity of marginally outer trapped surfaces (MOTS) in four-dimensional Reissner-Nordström (RN) spacetime. This is connected to studying the first-order derivative of the stability operator (and hence the second derivative of the outgoing null expansion). Stability means that the principal eigenvalue is non-negative, and rigidity means that we cannot deform MOTS. The question we have addressed in this thesis is distinguishing between stability and rigidity. We study the special case of the inner horizon of Reissner-Nordström spacetimes for specific values of charge and mass is horizons can be unstable, and we ask questions whether they unstable is still rigid. To approach this question we use a technique to reduce an infinite-dimensional second variation calculation to a finite-dimensional one. We start with a brief introduction to general relativity and review some fundamental aspects of black holes. We then define the stability of MOTS in terms of the principal eigenvalue. Since the stability operator has a zero eigenvalue in our case, the MOTS admits infinitesimal deformations. In the rest of the work we use Lyapunov-Schmidt reduction to investigate whether these infinitesimal deformations can be made finite. We give evidence that suggests that the inner horizon is stable.

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