Classical and Quantum Thermodynamic Systems in Curved Spacetime

Abstract

Systems at finite temperature make up the vast majority of realistic physical scenarios. Indeed, although zero temperature is often accompanied by simpler mathematics, the richness in physical results is evident when one considers the system to have temperature and even more so if the background geometry is curved. This thesis will be dedicated to the study of this type of physical systems, where thermodynamics and general relativity equally contribute to the dynamics. The first part will be devoted to the study of classical thermodynamic systems in curved spacetime, namely thin matter shells at finite temperature. These objects partition spacetime into separate pieces, and their very existence is conditioned by the so-called junctions conditions. The latter conditions allow us to carefully study both the mechanical and thermodynamics of the shell and, in particular, they give rise to a well-defined notion of entropy. The shell can then be taken to its black hole limit, providing an alternative way to study black hole thermodynamics. We will do this for different geometries, obtaining as byproduct a plausible answer for the debated value of the entropy of an extremal black hole. In the second part we shall review the standard formalisms to study QFT in curved spacetimes, in order to explore quantum properties of thermodynamic systems in the presence of gravity. Massive quantum scalar fields at finite temperature will be the systems of choice, whereby various instances of vacuum polarisation will be calculated in a variety of black hole geometries. Both numerical and analytic results will be obtained, and new addition formulas for a certain class of transcendental functions will be derived. This part will culminate with a careful numerical study of symmetry restoration of a self-interacting scalar field around a charged black hole, where we verify insights present in the literature.

PhD thesis, Instituto Superior Tecnico, December 2018. 189 pages

References in corpus (16)

• Lectures on Holographic Superfluidity and Superconductivity
• Non-relativistic holography
• Black holes in asymptotically Lifshitz spacetime
• AdS/Ricci-flat correspondence and the Gregory-Laflamme instability
• Entropy of extremal black holes from entropy of quasiblack holes
• A Mode-Sum Prescription for Vacuum Polarization in Odd Dimensions
• A Mode-Sum Prescription for Vacuum Polarization in Even Dimensions
• Vacuum polarization in asymptotically anti-de Sitter black hole geometries
• Entropy of a self-gravitating electrically charged thin shell and the black hole limit
• DeWitt-Schwinger Renormalization and Vacuum Polarization in d Dimensions
• Entropy of thin shells in a (2+1)-dimensional asymptotically AdS spacetime and the BTZ black hole limit
• Vacuum polarization near asymptotically anti-de Sitter black holes in odd dimensions
• Radiation from a D-dimensional collision of shock waves: higher order set up and perturbation theory validity
• Hyperentropic systems and the generalized second law of thermodynamics
• Quantum buoyancy, generalized second law, and higher-dimensional entropy bounds
• Black Hole Quantum Vacuum Polarization in Higher Dimensions