Abstract
Black hole (BH) ringdowns provide a promising avenue for testing general relativity (GR) in the strong-field regime through quasi-normal modes (QNMs). In modified theories of gravity, the ringdown spectrum can deviate from its GR counterpart, potentially leading to observable signatures such as paritydependent frequency shifts and the breaking of isospectrality. The primary aim of this thesis is to investigate whether such effects can be identified in shift-symmetric Einstein–scalar–Gauss–Bonnet (EsGB) gravity using fully nonlinear numerical relativity (NR) simulations, and whether they remain detectable at weak coupling and limited numerical resolution.
Axisymmetric simulations of perturbed BHs are evolved in both GR and EsGB using a modified generalized harmonic formulation of the Einstein equations. Separate and combined even– (polar) and odd–parity (axial) perturbations are considered across a range of initial spins χ0 and dimensionless Gauss– Bonnet couplings λ/M02 . Fundamental (ℓ,m) = (2, 0) ringdown frequencies are extracted from waveforms extrapolated to spatial infinity by fitting exponentially damped sinusoids to the late-time signal, while systematically varying the fitting procedure and numerical resolution to assess robustness.
The GR simulations reproduce the expected Schwarzschild and Kerr QNM spectra with sufficient accuracy at the production resolution and provide important benchmarks for interpreting the EsGB results. For all configurations except the weakest-coupling case, (χ0, λ/M02) = (0.99, 0.02), the fitted complex frequencies exhibit parity-dependent shifts that exceed the estimated fitting uncertainties. The magnitudes of these deviations from GR are qualitatively consistent with perturbative predictions for the (2, 1) and (2, 2) modes from the literature, while direct comparisons of the frequencies in the non-spinning case show agreement within fitting uncertainties. Resolution studies demonstrate that small deviations at weak coupling can disappear under refinement, whereas larger-coupling configurations retain clear polar–axial separation at higher resolution. Simultaneous extraction of distinct polar and axial contributions from combined waveforms is found to be substantially more difficult due to fitting degeneracies.
The results support the interpretation that parity-dependent modifications of the ringdown spectrum become detectable in sufficiently high-resolution nonlinear EsGB simulations, particularly for larger couplings. At the same time, the resolution studies suggest that resolving comparably small beyond- GR effects in fully three-dimensional binary merger simulations may prove significantly more challenging due to their substantially higher computational cost and correspondingly lower achievable resolutions. More broadly, the work demonstrates the potential of nonlinear NR simulations in modified gravity as a tool for probing strong-field deviations from GR through BH ringdowns.
Supervisors:
- David Fonseca Mota, Professor at Institute of Theoretical Astrophysics, UiO
- Maxence Corman, Postdoctoral fellow at Max Planck Institute for Gravitational Physics
Intern. assessor: Boris Vilhelm Gudiksen, Professor at Institute of Theoretical Astrophysics, UiO
Extern. assessor: Jose Beltran Jimenez, Professor at University of Salamanca