Trapping of light in stationary spacetimes

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Dokumentart: Dissertation
Date: 2019-10-11
Language: English
Faculty: 7 Mathematisch-Naturwissenschaftliche Fakultät
Department: Mathematik
Advisor: Cederbaum, Carla (Prof. Dr.)
Day of Oral Examination: 2019-09-27
DDC Classifikation: 510 - Mathematics
Keywords: Relativitätstheorie
Other Keywords: Reissner-Nordström
stationäre Raumzeiten
photon sphere
photon region
trapped light
stationary spacetimes
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We study phenomena related to trapping of light in stationary spacetimes. We first prove a uniqueness result for ‘quasilocal photon spheres‘ and static horizons in asymptotically flat so-called pseudo-electrostatic systems. Our result implies that an asymptotically Reissner--Nordström electrostatic system of arbitrary dimension which contains a ‘subextremal‘ photon sphere is a Reissner--Nordström manifold. The methods used in the proof of this theorem go back to the classical black hole uniqueness proofs of Bunting and Masood-ul-Alam and Ruback, whose techniques we combine with newer ideas developed by Cederbaum--Galloway and Cederbaum. In the second part, we leave the static setting and investigate trapped light in the Kerr spacetime. We give a new and (compared an earlier result by Dyatlov) more direct proof that the photon region in the Kerr spacetime can be naturally understood as a submanifold of the phase space and has topology SO(3)xR.

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