A Semi-classical Spacetime Region with Maximum Entropy

演講地點 : RM36567

Abstract:
What is the maximum entropy that can be given a finite region?
What is the structure of such a spacetime? These questions should be related to
searching for fundamental degrees of freedom in quantum gravity, as
entropy is generally associated with the underlying microscopic degrees of
freedom. In this talk, we consider a 4D spherically-symmetric static
spacetime region as a collection of quanta in the semi-classical Einstein
equation and study the entropy including the self-gravity. For sufficiently
excited states, we estimate the entropy using a WKB-like method and obtain
its upper bound. The saturation condition uniquely determines the entropymaximized
spacetime as a dense configuration with near-Planckian
curvatures and a surface just outside the Schwarzschild radius, and the
metric is a non-perturbative solution for Planck constant. The maximum
entropy then saturates the Bousso bound and coincides with the Bekenstein-
Hawking formula, which thus verifies the Bousso bound. [arXiv:
2309.00602 (ver2)]