Speaker
Description
One property that characterizes a black hole is that it maximizes entropy in a finite region with a fixed surface area. It may be a more fundamental one than the existence of a horizon in the context of quantum gravity, where there is no notion of continuum geometry. Using this characterization, we consider the interior of a black hole in the 4D semi-classical Einstein equation. For simplicity, we consider spherical static finite configurations for various sufficiently excited quantum states, apply thermodynamic typicality to a small subsystem, and estimate entropy including self-gravity, to derive its upper bound. By the saturation condition and consistency with local thermodynamics, the entropy-maximized configuration is uniquely determined as a radially uniform dense configuration with near-Planckian curvatures and a surface just outside the Schwarzschild radius. The interior metric is a non-perturbative self-consistent solution in the Planck constant. The maximum entropy, given by the volume integral of the entropy density, becomes the Bekenstein-Hawking formula due to the strong self-gravity, yielding the Bousso bound. Thus, this compact dense configuration may be a candidate for black hole in quantum theory. We finally discuss some similarities to quantum gravitational condensation in group field theory.