Black Hole Uncertainties

TL;DR

This paper investigates the quantum properties of two-dimensional dilaton black holes using the Wheeler-DeWitt equation, revealing uncertainty relations between black hole mass and Hawking flux parameters, akin to string theory uncertainties.

Contribution

It introduces a quantum framework for black hole wave functions and uncovers a novel uncertainty relation specific to black hole parameters.

Findings

Uncertainty relations exist for black hole mass and Hawking flux parameters.

Only at a specific parameter value can both quantities be precisely known.

A relation similar to string uncertainty principles is derived for generic cases.

Abstract

In this work the quantum theory of two dimensional dilaton black holes is studied using the Wheeler De Witt equation. The solutions correspond to wave functions of the black hole. It is found that for an observer inside the horizon, there are uncertainty relations for the black hole mass and a parameter in the metric determining the Hawking flux. Only for a particular value of this parameter, can both be known with arbitrary accuracy. In the generic case there is instead a relation which is very similar to the so called string uncertainty relation.