Exploring Black Hole Entropy, Spacetime Perturbations, and Their Applications in Astrophysics

Abstract Tidal deformations and quasinormal frequencies result when a black hole experiences a perturbation to its geometry, such as by a small mass or a field. These effects can be measured experimentally from gravitational wave data or calculated mathematically using various methods. This paper details various studies that were done to develop meaningful and accurate calculations of tidal Love numbers and quasinormal frequencies, as well as the motivations for such efforts. In addition, various attempts to formulate a more sound interpretation of black hole entropy are discussed, including the shortcomings of some and the significance of these efforts in other areas of study. In general, the topics and studies analyzed in this paper are fundamental in the development of the theory of quantum gravity, and in the analysis of gravitational wave data, both of which can be used to help us better understand black holes.