Black hole complementarity with the generalized uncertainty principle in gravity's rainbow

TL;DR

This paper investigates how the generalized uncertainty principle and gravity's rainbow affect black hole complementarity, showing that the no-cloning theorem remains valid under these quantum gravity modifications.

Contribution

It demonstrates that black hole complementarity and the no-cloning theorem hold even when incorporating the generalized uncertainty principle and gravity's rainbow effects.

Findings

Duplication of information is forbidden under the generalized uncertainty principle.

Black hole complementarity remains valid with gravity's rainbow modifications.

The no-cloning theorem can be upheld in this quantum gravity framework.

Abstract

When gravitation is combined with quantum theory, the Heisenberg uncertainty principle could be extended to the generalized uncertainty principle accompanying a minimal length. To see how the generalized uncertainty principle works in the context of black hole complementarity, we calculate the required energy to duplicate information for the Schwarzschild black hole. It shows that the duplication of information is not allowed and black hole complementarity is still valid even assuming the generalized uncertainty principle. On the other hand, the generalized uncertainty principle with the minimal length could lead to a modification of the conventional dispersion relation in light of Gravity's Rainbow, where the minimal length is also invariant as well as the speed of light. Revisiting the gedanken experiment, we show that the no-cloning theorem for black hole complementarity can be made valid in the regime of Gravity's Rainbow on a certain combination of parameters.