Wydarzenia

Seminarium Fizyki Politechniki Wrocławskiej

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

Prof. José P. S. Lemos

Physics Department, University of Lisbon

Microscopic gravitational systems containing black holes and radiation exhibit quantum and thermodynamic behavior that deserves detailed investigation. Quantum fluctuations near a black hole's event horizon cause it to emit radiation at the Hawking temperature, gradually losing mass and evaporating completely. Black holes and radiation are therefore intrinsically linked, both quantum mechanically and gravitationally. To study this interconnection, we consider self-gravitating radiation enclosed in a finite box whose walls are maintained at a fixed temperature, thereby providing a well-defined canonical ensemble. While black holes in such a cavity have been extensively studied, the properties of hot self-gravitating radiation in this setting remain unexplored. To bridge this gap, we construct the canonical ensemble of self-gravitating radiation using the Euclidean path-integral approach to quantum gravity. At leading semiclassical, i.e., zero-loop order, we evaluate the Euclidean gravitational-matter action to obtain the partition function, determine the equilibrium configurations, i.e., the solutions, and analyze their stability. Within this framework, we uncover the complete phase structure of the radiation ensemble. We find that only one branch of solutions is simultaneously thermodynamically and mechanically stable and thus provides a consistent zero-loop approximation. We then compute the important thermodynamic quantities of the radiation, namely, the free energy, entropy, energy, and heat capacity. We find that positivity of the heat capacity alone is not sufficient to ensure the validity of the semiclassical approximation, highlighting the power of the Euclidean path-integral formalism. Finally, we compare the Euclidean actions of self-gravitating radiation and black-hole configurations at fixed box radius and temperature to investigate phase transitions. Previous analyses of black-hole nucleation have typically compared stable black holes with hot flat space. Once the self-gravity of the radiation is properly taken into account, however, the background is no longer flat but curved. In flat space, thermal equilibrium with a uniform temperature can always be maintained. On the other hand, we find that self-gravitating radiation admits no equilibrium solutions above a certain temperature. Consequently, phase transitions between hot curved-space configurations and black-hole states are substantially more constrained and can occur only at or below the Planck temperature.