Rainbow gravity corrections to the information flux of a black hole and the sparsity of Hawking radiation

TL;DR

This paper investigates how rainbow gravity modifies the information flux and sparsity of Hawking radiation from black holes, revealing significant effects near the Planck scale and suggesting the existence of black hole remnants.

Contribution

It introduces the impact of rainbow gravity on black hole information flux and radiation sparsity, highlighting quantum gravity effects during black hole evaporation.

Findings

Rainbow gravity significantly affects information flux near Planck scale.

The entropy loss per emitted quantum approaches zero as black hole mass decreases.

Hawking radiation sparsity diverges at the end of evaporation, indicating a remnant formation.

Abstract

In this paper, by utilizing the rainbow functions that were proposed by Amelino-Camelia \emph{et al}., the information flux of rainbow Schwarzschild black hole and the sparsity of Hawking radiation in rainbow gravity are explored. The results show that the rainbow gravity has a very significant effect on the information flux. When the mass of rainbow Schwarzschild black hole approaches to the order of Planck scale, the Bekenstein entropy loss per emitted quanta in terms of the mass of Schwarzschild black hole reduces to zero. Furthermore, we also find the sparsity of Hawking radiation in rainbow gravity is no longer a constant; instead, it monotonically decreases as the mass of black hole decrease. At the final stages of evaporation, the modified sparsity becomes infinity, which indicates the effect of quantum gravity stops Hawking radiation and leads to remnant.