Black Holes beyond Relativity: the Onset of Chaos in Stellar Inspirals
Velden, Justus van der
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With general relativity’s incompatibility with quantum field theory forming our generation’s primary challenge in high energy theoretical physics research, the upcoming LISA gravitational wave experiment will provide exciting new avenues to test for novel theories of gravity. One method of testing general relativity in the strong-field regime is the study of the dynamics and orbital evolution of a stellar-mass object’s inspiral into a supermassive black hole in different gravity theorems and searching for observable differences. In this thesis, a theoretical framework is presented in which to study the potentially chaotic properties of these extreme mass-ratio inspirals. The derivations, advantages and disadvantages of different formulations of black hole solutions in general relativity are considered. A treatment of orbits in the Kerr spacetime is performed in a broad range of scenarios. The framework is then employed to determine the existence and nature of the onset of chaotic features in the orbital dynamics of general relativity and Einstein-dilaton Gauss-Bonnet theory, a proposed theory of modified gravity derived from string theory. By employin numerical integration methods, we find that high-accuracy approximations of the metric tensor are required to determine whether chaotic features exist in modified gravity. By using approximate analytical black hole solutions, we find that the radial width of these features and hence the deviations from Kerr are of order r ≈ O(10−4) or smaller in Boyer-Lindquist coordinates. An investigation into a coordinate-independent quantification of chaotic features is performed and applied to the findings. The results are then presented in the context of astrophysical challenges and experimental implications, based on which we conclude that future work is needed to conclusively determine whether these features are detectable.