Black holes and self-gravitating matter at micro scales: Quantum and thermodynamic properties

by José Pizarro de Sande e Lemos (Physics Department, University of Lisbon)

Friday 20 Jun 2025, 14:00 → 15:30 Europe/Rome

Aula Careri (Dip. di Fisica - Edificio G. Marconi)

Microscopic gravitational systems containing black holes and matter exhibit rich quantum and thermodynamic behavior that calls for detailed investigation. Due to vacuum fluctuations near a black hole's event horizon, particles, such as gravitons and matter fields, can be emitted to infinity at the Hawking temperature. This Hawking radiation causes the black hole to lose mass over time and may ultimately lead to its complete evaporation. To explore the interaction between black holes and hot matter, we consider such systems in anti-de Sitter (AdS) space at fixed temperature. AdS space acts as a confining geometry, effectively functioning as a true thermal reservoir and thereby providing a well-defined canonical ensemble in the context of statistical mechanics. While black holes in AdS space, most notably through the Hawking-Page phase transition, have been extensively studied, much less is known about the thermodynamics of hot self-gravitating matter in this setting. To address this gap, we construct the canonical ensemble for a hot, self-gravitating thin shell of matter in AdS space. Using the Euclidean path integral approach to quantum gravity, we compute the partition function at the leading semiclassical level by evaluating the Euclidean classical action. From this, we determine the equilibrium configurations of the shell and analyze their mechanical and thermodynamic stability. For specific equations of state for the shell's pressure and temperature, we solve the ensemble and uncover four distinct shell configurations. Among them, one solution is fully stable, both mechanically and thermodynamically. Our analysis reveals a first-order phase transition between the matter-dominated phase, represented by the stable shell, and the black hole phase of the Hawking-Page type. Additionally, we identify a critical maximum temperature beyond which no shell solutions exist, the shell is expected to dynamically collapse into a black hole. These findings, including the nature of the equilibrium solutions, the stability criteria, and the thermodynamic phase structure, will be discussed in detail during the seminar.