Quantum gravitational wave function for the interior of a black hole and the generalized uncertainty principle

TL;DR

This paper explores the quantum structure inside black holes by solving the Wheeler-DeWitt equation, revealing a bouncing point that challenges classical notions of time and linking it to the generalized uncertainty principle.

Contribution

It introduces a quantum model of black hole interiors with a bouncing wave function and discusses the implications for the arrow of time and spacetime structure.

Findings

Wave function exhibits a bounce around the black hole's core.

Quantum bounce leads to ambiguity in defining the arrow of time.

Conceptual link established between bounce and generalized uncertainty principle.

Abstract

We investigate the internal structures of a Schwarzschild black hole by solving the Wheeler-DeWitt equation. The generic bounded wave function has a bouncing point around $r \simeq M$, where $M$ is the black hole mass. Due to this quantum bouncing, there appears an ambiguity to define the arrow of time. If we introduce two arrows of time, one can then interpret that two classical spacetime is annihilated around the bouncing point. Finally, we provide a conceptual explanation based on the generalized uncertainty principle.