Hawking Radiation Under Generalized Uncertainty Principle

TL;DR

This paper investigates how the generalized uncertainty principle affects Hawking radiation, revealing that radiation ceases around the scrambling time without significantly changing the temperature, across different coordinate systems.

Contribution

It demonstrates that incorporating a minimal length scale into the background geometry suppresses Hawking radiation near the scrambling time, a novel insight into quantum gravity effects on black hole evaporation.

Findings

Hawking radiation stops near the scrambling time

Hawking temperature remains largely unchanged

Effect is consistent across different coordinate systems

Abstract

The generalized uncertainty relation is expected to be an essential element in a theory of quantum gravity. In this work, we examine its effect on the Hawking radiation of a Schwarzschild black hole formed from collapse by incorporating a minimal uncertainty length scale into the radial coordinate of the background. This is implemented in both the ingoing Vaidya coordinates and a family of freely falling coordinates. We find that, regardless of the choice of the coordinate system, Hawking radiation is turned off at around the scrambling time. Interestingly, this phenomenon occurs while the Hawking temperature remains largely unmodified.