Black Holes: Thermodynamics and Statistical Mechanics

In semiclassical gravity, black holes are real thermodynamic systems. The statement is not based on a single analogy, but rather on a web of results: horizon thermodynamics, Hawking radiation, Euclidean periodicity, gravitational partition functions, the generalized second law, and correct microscopic counts in the protected sectors. For Schwarzschild black holes,,, and. These relations account for the black holes in the universe and the black holes in the universe's asymptotic region. The stability, phase behavior, and the rest are all environmental and ensemble dependent. Black holes with charge, rotation, finite cavities, and AdS boundary conditions distinguish branches with different heat capacities and free energies. When considering the AdS boundary as a pressure, liquid–gas-like behavior and critical phenomena emerge. This strongly suggests that black-hole thermodynamics is a rich and complex system beyond landscape constraining. At a global level, the microscopic problem remains open. String/D-brane counting provides a connection between the Bekenstein–Hawking entropy and the logarithm of quantum level degeneracy, but this is mainly applicable to certain extremal or near-extremal cases. The horizon state, entanglement, and the rest provide different approaches for the area law and through various state spaces. Their convergence supports the area law, while their differences indicate that for astrophysical black holes, the underlying degrees of freedom have not been determined. With respect to the information problem, generalized entropy, quantum extremal surfaces and islands, have been helpful in understanding the problem as a whole. These concepts, in controlled semi-classical models, recapture the unitary Page curve and show how the interior black hole can be included within the radiation entanglement wedge. Recent work done well outside of equilibrium has shown that reasoning of the first law can be applied to dynamical horizons. Black holes are still the best places to study how the quantum of spacetime and the statistical nature of spacetime, as well as the structure of entanglement and information, might be defined.

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