Black Hole from Entropy Maximization

• URL: http://arxiv.org/abs/2309.00602v4
• Date: Fri, 2 Aug 2024 02:57:52 GMT
• Title: Black Hole from Entropy Maximization
• Authors: Yuki Yokokura,
• Abstract summary: One quantum characterization of a black hole motivated by (local) holography and thermodynamics is that it maximizes thermodynamic entropy for a given surface area. We explore this possibility by solving the 4D semi-classical Einstein equation with many matter fields, and find a picture of a black hole. For spherical static highly-excited configurations, we apply local typicality and estimate the entropy including self-gravity to derive its upper bound.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: One quantum characterization of a black hole motivated by (local) holography and thermodynamics is that it maximizes thermodynamic entropy for a given surface area. In the context of quantum gravity, this could be more fundamental than the classical characterization by a horizon. As a step, we explore this possibility by solving the 4D semi-classical Einstein equation with many matter fields, and find a picture of a black hole. For spherical static highly-excited configurations, we apply local typicality and estimate the entropy including self-gravity to derive its upper bound. The saturation condition uniquely determines the entropy-maximized configuration: self-gravitating quanta condensate into a radially-uniform dense configuration with no horizon, where the self-gravity and a large quantum pressure induced by the curvatures are balanced and no singularity appears. The interior metric is a self-consistent and non-perturbative solution for Planck's constant. The maximum entropy, given by the volume integral of the entropy density, agrees with the Bekenstein-Hawking formula through self-gravity, deriving the Bousso bound for thermodynamic entropy. Finally, 10 future prospects are discussed, leading to the speculative view that the configuration represents semi-classically a quantum-gravitational condensate with holographic bulk dynamics.

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