Classical and quantum bosonic fields on the spacetimes of black holes and stars

This thesis consists of two parts. Part I, containing chapters 2, 3 and 4, concerns classical, massive, scalar and vector (Proca) fields on static and rotating black hole spacetimes. Part II, containing chapters 5, 6 and 7, concerns quantum, massless, scalar fields on static black hole spacetimes and the spacetimes of spherically symmetric stars. The goal of Part I is to present our numerical calculation of the quasinormal modes (QNMs) of the odd-parity, charged Proca field on the Reissner-Nordström spacetime and all three polarization states of the uncharged Proca field on the Kerr and Kerr-Newman spacetimes. In chapter 2 we introduce the static and rotating black hole spacetimes we will be concerned with and the formalism used to describe the propagation of scalar and vector fields on these spacetimes. Then, in chapter 3, we discuss the known methods of solving the equations of motion of these fields on static spacetimes and how this leads to the concept of QNMs, including our new application of Leaver’s method to the odd-parity, charged Proca field on the Reissner-Nordström spacetime. Finally, chapter 4 details the much more recent method (the LFKK ansatz) used to solve the Proca equation of motion on rotating black hole spacetimes and our new application of Leaver’s method to the uncharged Proca field on the Kerr and Kerr-Newman spacetimes. The focus of Part II is on our numerical exploration of the method of taking differences between quantum expectation values (QEVs) evaluated in the same vacuum state, but on different background spacetimes. In chapter 5 we introduce the concept of semiclassical gravity and the method of Levi and Ori for calculating QEVs, including the results of our own numerical implementation of said method that are consistent with the literature. Then, in chapter 6, we discuss the method of Anderson and Fabbri to find the differences of the vacuum polarization and stress-energy tensor of a scalar field between the spacetimes of a Newtonian star and a black hole in the Boulware vacuum state. We apply this method to a toy model consisting of an infinitesimally thin shell on a flat background spacetime. In chapter 7, we extend this method to more general spherically symmetric stellar models and verify our new results numerically. We also present a new numerical analysis of the vacuum polarization and stress-energy differences near the star surface and consider its dependence on the star structure and the coupling to the scalar curvature. Finally, chapter 8 contains our conclusions and ideas for possible extensions to the work presented here.