Quantum black holes: inside and outside

TL;DR

This paper investigates the quantum structure of black holes using the Wheeler-DeWitt equation, revealing that the interior must be a superposition of states, implying a highly quantum nature and providing insights into the information loss paradox.

Contribution

It demonstrates that coherent states cannot cross the event horizon, suggesting the interior is a superposition of states, thus offering a new perspective on black hole quantum structure.

Findings

Wave function must be annihilated near the horizon

Interior is a superposition of coherent states

Black hole is a highly quantum macroscopic object

Abstract

For a unitary description of an evaporating black hole, one usually chooses the time slices that cover only outside of the event horizon, which is mostly problem-free because the event horizon is not encountered. However, is there any justification for avoiding time slices that cover inside the event horizon? To answer the question, we investigate the Wheeler-DeWitt equation, where the time slices can cover both inside and outside the event horizon. We find that one can reasonably construct a wave packet that covers outside, but the wave function must be annihilated near the event horizon. This observation strongly suggests that we cannot choose a coherent state for a spacelike hypersurface that crosses the event horizon. To explain the unitary time evolution, we must keep the slices as coherent states; hence, they must always be outside the event horizon. In contrast, inside the horizon, we cannot have a single coherent state of a classical spacetime. Hence, the interior must be a superposition of several coherent states, which implies that there exists a horizon-scale uncertainty and a black hole should be viewed as a highly quantum macroscopic object. We provide a synthetic approach to understanding the information loss paradox from this perspective.