Quantum Fields in Curved Spacetimes: From Detector Entanglement to Black Hole Thermodynamics

Abstract

This thesis presents two independent investigations into quantum field theory in curved spacetime. The first concerns relativistic quantum information, with a focus on entanglement harvesting and detector-based probes of quantum fields in curved spacetimes. The second addresses semiclassical aspects of black hole thermodynamics in AdS braneworld settings, incorporating the backreaction of quantum fields to all orders of perturbation theory, and extending previous studies of quantum black holes to include both charge and spin. In Part I, we study the entanglement of quantum fields in curved spacetime, using localized particle detectors interacting with a scalar field. We analyze scenarios involving both flat and curved backgrounds, including gravitational shock waves, the BTZ black hole, and general dimensional anti–de Sitter and de Sitter spacetimes. For the case of initially entangled detectors, we find that interactions with the field can lead to either degradation or amplification of entanglement, depending on the initial state and spacetime geometry. We further derive exact expressions for density matrix elements, at the lowest perturbative order, in the form of infinite analytical series, for detectors on static worldlines in various spacetimes. The transition rate of an in-falling detector in the BTZ black hole spacetime is also derived as an infinite series. These analytic results allow for exact evaluation of quantities, namely the entanglement measures of concurrence and negativity, which are typically computed numerically. In addition, we provide a new example of the ability of detectors to distinguish topologically distinct spacetimes which are locally identical outside of horizons, focusing on the ℝP² and Swedish geons built from the BTZ spacetime. Our results show that localized measurements are sensitive not only to curvature but also to topological features of the underlying geometry. Part II is concerned with the construction and thermodynamic analysis of quantum-corrected black holes in a doubly holographic braneworld model. We obtain a charged and rotating solution localized on an AdS₃ brane embedded in an AdS₄ bulk, incorporating the full backreaction from conformal fields to all orders of perturbation theory. We compute the thermodynamic properties of these black holes, and examine their behavior in extended thermodynamic phase space where the cosmological constant is a variable. We find that the inclusion of charge or spin removes re-entrant phase transitions present in the neutral-static case, and that the critical exponents of these objects match those predicted by classical mean-field theory. The re-entrant phase transitions of the neutral-static quantum black hole has critical exponents which differ from the mean-field values