Some aspects of black hole physics: spherical null and timelike orbits, and event horizon detection

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2021-9-08
Tavlayan, Aydın
In this thesis, some crucial aspects of black hole physics are investigated. Exact formulas relating the radius of the spherical photon orbits to the black hole's rotation parameter and the effective inclination angle of the orbit have been known only for equatorial and polar orbits up to now. In the first chapter, an infinite family of exact formulas is provided for non-equatorial orbits that lie between these extreme limits. The sextic polynomial equation in the photon radius, derived from the geodesic equations, is studied to arrive at these novel analytical solutions. In the second chapter, the method developed to investigate the spherical orbits is modified in order to analyze the timelike orbits of the massive particles. For both null and timelike orbits, some approximate solutions are derived with the help of the Lagrange-Bürmann theorem, which provides a great understanding of the behavior of particles in the vicinity of a black hole. In the last part, an invariant characterization of event horizons of black holes is provided. As already known, some judiciously chosen local curvature scalars can be used to invariantly characterize event horizons of black holes in D > 3 dimensions. However, they fail for the three-dimensional Bañados-Teitelboim-Zanelli (BTZ) black hole since all curvature invariants are constant. Here, an invariant characterization of the event horizon of the BTZ black hole using the curvature invariants of codimension one hypersurfaces, instead of the full spacetime, is provided. The method developed in this work is also applicable to black holes in generic dimensions, but is most efficient in three, four, and five dimensions. Four-dimensional Kerr, five-dimensional Myers-Perry, three-dimensional warped-anti-de Sitter, and the three-dimensional asymptotically flat black holes are given as examples.

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Citation Formats
A. Tavlayan, “Some aspects of black hole physics: spherical null and timelike orbits, and event horizon detection,” M.S. - Master of Science, Middle East Technical University, 2021.