2023/09/01 by Yuki Yokokura, Yokokura, Yuki · 2 citations
Physics and Astronomy · #Cosmology and Gravitation Theories #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories
paper · pdf · doi:10.48550/arxiv.2309.00602
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. For highly-excited spherically-symmetric static 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 in 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 a speculative view that the configuration represents a quantum-gravitational condensate in a semi-classical manner.