Black Hole Solutions and Gravitational Waveform Modeling in General Relativity and Beyond 16 views

Gravitational-wave observations provide a powerful way to test general relativity in the strong-field, dynamical regime, but doing so requires waveform models that are both accurate and computationally efficient. One also needs to know black hole solutions in theories of gravity that one wishes to test against with gravitational waves from binary black hole coalescences. The first part of the thesis develops analytical and semi-analytical tools for modeling compact-binary signals in general relativity. A central part of this work improves the hybrid gravitational-wave framework for comparable-mass, nonspinning binary black holes by matching post-Newtonian information in the near zone to black-hole perturbation theory in the exterior region across a timelike worldtube. By introducing phenomenological refinements to the shell trajectory, boundary data, and effective potential, the resulting inspiral-merger-ringdown waveforms achieve significantly better agreement with numerical-relativity results. The second part of the thesis extends this hybrid framework beyond general relativity to Einstein-dilaton Gauss-Bonnet gravity. Einstein-dilaton Gauss-Bonnet gravity is inspired by string theory and has a scalar field coupled to higher-curvature terms in the extended Einstein-Hilbert action. We calibrated effective potentials and boundary data that are used to model scalar radiation from binary black holes and to reproduce key features of numerical results. The final part of the thesis studies black-hole solutions in higher-derivative Einstein-Maxwell theories using modern scattering-amplitude methods. By extracting the classical limit of amplitudes generated by curvature-photon interactions, we derive corrections to charged black-hole geometries and relate them to effective field theory operators such as $RF^2$-type terms. This provides a complementary perspective on black-hole structure, linking quantum-field-theoretic methods to classical spacetime solutions. Taken together, this thesis improves gravitational waveform modeling, develops new ways to study possible deviations from general relativity, and shows how waveform modeling and scattering amplitudes can help us better understand compact objects and strong-gravity dynamics.

PHD (Doctor of Philosophy)

English

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2026-05-05