On thermodynamics of compact objects

With the recent progress in observations of astrophysical black holes, it has become more important to understand in detail the physics of strongly gravitating horizonless objects. If the objects identified in the observations are indeed horizonless and ultracompact, high curvature effects may come into play, and their explorations may be intimately related to new physics beyond General Relativity (GR). In this paper, we revisit the concept of statistical thermodynamics in curved spacetime, focusing on self-gravitating compact systems without event horizons. Differently from the previous studies in this context, we develop a generic framework with no explicit dependence on the gravitational field equations, which is then applicable to a general theory of gravity. Defining the global variables directly from the local counterparts, the conventional thermodynamics follows for a generic curved spacetime. The key step is the appropriate identification of thermodynamic volume to ensure the first law of thermodynamics, which is in general different from the geometric volume. For demonstration, we consider familiar examples of self-gravitating gas in GR, where the connection to previous studies becomes clear. We also discuss 2-2-holes in quadratic gravity, a novel example of black hole mimickers that features super-Planckian curvatures in the interior. When the physical mass is treated as the total internal energy, interesting connections to black hole thermodynamics emerge. We find universal high curvature effects in thermodynamics for these objects, and the dominant effects happen to be conveniently encoded in the thermodynamic volume.
Comment: 26 pages, 3 figures