The quantum relative entropy of the Schwarzschild black-hole and the area law
arXiv:2501.09491 · doi:10.3390/e27030266
Abstract
The area law obeyed by the thermodynamic entropy of black holes is one of the fundamental results relating gravity to statistical mechanics. In this work we provide a derivation of the area law for the quantum relative entropy of the Schwarzschild black-hole for arbitrary Schwarzschild radius. The quantum relative entropy between the metric of the manifold and the metric induced by the geometry and the matter field has been proposed in G. Bianconi "Gravity from entropy", Phys. Rev. D (2025) as the action for entropic quantum gravity leading to modified Einstein equations. The quantum relative entropy generalizes Araki entropy and treats the metrics between zero-forms, one-forms, and two-forms as quantum operators. Although the Schwarzschild metric is not an exact solution of the modified Einstein equations of the entropic quantum gravity, it is an approximate solution valid in the low coupling, small curvature limit. Here we show that the quantum relative entropy associated to the Schwarzschild metric obeys the area law for large Schwarzschild radius. We provide a full statistical mechanics interpretation of the results.
(7 pages,2 figures)
References in corpus (14)
- A Spin Entanglement Witness for Quantum Gravity
- Gravitationally-induced entanglement between two massive particles is sufficient evidence of quantum effects in gravity
- Measurement of stimulated Hawking emission in an analogue system
- Testing the black-hole area law with GW150914
- Non-Gaussianity as a signature of a quantum theory of gravity
- Interferometric Unruh detectors for Bose-Einstein condensates
- Quantum Gravitational Corrections to the Entropy of a Schwarzschild Black Hole
- A Bi-Metric Theory with Exchange Symmetry
- Gravity from entropy
- From spin foams to area metric dynamics to gravitons
- Horizon entanglement area law from regular black hole thermodynamics
- Entanglement area law violation from field-curvature coupling
- Area-metric gravity revisited
- Quantum Theory, Gravity and Second Order Geometry