Black Hole from Entropy Maximization

Tuesday 8 Oct 2024, 09:00 → 10:30 Asia/Tokyo

Date: October 8 (Tue), 9:00(JST)
Speaker: Yuki Yokokura (RIKEN)
Title: Black Hole from Entropy Maximization

Abstract: The identity of a black hole is still mysterious theoretically and observationally. It has the thermodynamic entropy (the Bekenstein-Hawking entropy). According to quantum theory and thermodynamics, the origin of thermodynamic entropy is quantum mechanical. Therefore, a black hole should be essentially a quantum object. So, what is the quantum definition/characterization of black holes? One candidate motivated by (local) holography and thermodynamics is that a black hole maximizes thermodynamic entropy for a given (expectation value of) surface area. As a step toward exploring this possibility, we study the entropy of various highly-excited spherical static configurations in the 4D semi-classical Einstein equation with many matter fields, and reach uniquely the entropy-maximizing configuration. That is, 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 exactly with the Bekenstein-Hawking formula through the self-gravity, leading to the Bousso bound for thermodynamic entropy. Finally, we see a speculative view that the configuration represents semi-classically a quantum-gravitational condensate. [arXiv:2309.00602]