Quasi-Normal Modes of Black Holes in Quantum Gravity

Overview & Synopsis

The first direct detection of Gravitational Waves in 2015 by the LIGO experiment was a major breakthrough in our understanding of gravity. By measuring the Gravitational Wave signal emitted during the merge of two Black Holes and comparing it to the theoretical predictions, it is now possible to test General Relativity in the strong gravity regime. Even though no deviation from the predictions of Einstein's theory has been detected, there is still great hope of finding disparities with the expected future new detectors (LISA, Einstein Telescope, Cosmic Explorer).In this thesis we are interested in the ringdown part of the Gravitational Wave signal, characterised by complex frequencies called the Quasi-Normal Modes. These frequencies govern the return to equilibrium of the perturbed Black Hole and are only sensitive to the characteristics of the Black Hole itself and of the theory ruling its dynamics. It is therefore of great interest to study the Quasi-Normal Modes in different theories of gravity, and see how the structure and the symmetries are modified. This can have two benefits: first, test and discriminate new theories of gravity and BH models, and second, predict what kind of deviations could be detected from Gravitational Wave signals.This work aimed to focus on a non-perturbative and backgroundindependent approach to quantizing general relativity: the Loop Quantum Gravity, and to analyse the Quasi-Normal Modes of different Black Hole models developed from this theory. We selected different models of BHs and studied the scalar and gravitational test-field perturbations on their metric. We then computed the related Quasi-Normal Modes thanks to different numerical and analytical methods of computations, trying to span the largest part of the spectra possible. The deviations from General Relativity and the new interesting patterns were studied extensively.During the process, we were faced with a question regarding the meaning to be attributed to the spin 2 test-field perturbations. Indeed, in the case of Loop Quantum Gravity and any other theory of quantum gravity, no equivalent of the Einstein field equations were derived. The Black Hole models are effective solutions build using concepts, tools and methods from Loop Quantum Gravity. The study of Quasi-Normal Modes for these types of Black Holes thus only shows the impact of Black Hole metric corrections but not of space-time dynamics corrections. Besides, the link with the Gravitational Waves emitted from Black Holes is not evident. With this question in mind, we wanted to directly compare test-field perturbations and physical gravitational ones for a “simple” Black Hole in modified gravity for which the computation of these two types of perturbations is possible. Our choice came on the BCL BH, derived from Scalar-Tensor theories, for which the physical gravitational QNMs have already been computed. We then studied the test-field QNMs of this BH and described the differences arising between the two types of perturbations.