Thermodynamics in a gravitational field
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Date
2024-10-01
Authors
Σουρτζίνου, Ειρήνη-Τριανταφυλλιά
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Abstract
A major challenge in theoretical physics is to understand the interplay between general relativity and thermodynamics. A thermodynamic theory that incorporates gravity, is compatible with our cosmological history and includes black holes is still missing. An important step in this direction has been the generalized second law (GSL) of thermodynamics, which asserts that the sum of matter entropy and of a fraction of the black hole area is non-decreasing. To safeguard this law against challenges, Bekenstein proposed a universal bound to the entropy-to-energy ratio. In this thesis, we undertook a first-principles analysis of a paradigmatic system in the study of the GSL in black holes, a quantum ideal gas in a small box hovering over the Schwarzschild horizon. We first analysed the simpler case of a non-relativistic gas in a gravitational field, in order to understand the changes that we need to make in the thermodynamic description. Then, we analysed a constantly accelerating box of gas in Rindler spacetime, before focusing in our intended case. In our analysis, we described the gas in terms of free quantum fields, bosonic and fermionic, massive and massless, and we identified its thermodynamic properties through the microcanonical distribution. We showed that the physics depends strongly on the distance of the box from the horizon, which we treated as a {\em macroscopic} thermodynamic variable. We found that the system transitions from three-dimensional to two-dimensional as we approach the horizon, and that the pressure is highly anisotropic. Crucially, we showed that Bekenstein's bound fails generically in this system, which implies that a severe challenge to the GSL remains unresolved. We also found that the pressure difference between the upper and lower wall leads to an effective buoyant force that partially relieves the box of its weight. Finally, we demonstrated that the approximation of quantum fields propagating on a fixed background for matter breaks down when the system is brought to microscopic distances from the horizon, in which case backreaction effects must be taken into account.
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Keywords
Black hole thermodynamics, Entropy bounds, Generalized second law, Quantum ideal gases