Black Hole Complementarity in Gravity's Rainbow

TL;DR

This paper investigates how gravity's rainbow modifies black hole complementarity by calculating the energy needed for information duplication, revealing a critical rainbow parameter value that preserves quantum mechanics consistency.

Contribution

It introduces a critical rainbow parameter value in gravity's rainbow that affects black hole complementarity and the potential for information duplication.

Findings

Critical rainbow parameter limits information duplication.

Duplication may be possible above the critical value.

Model requires additional constraints for certain rainbow parameters.

Abstract

To see how the gravity's rainbow works for black hole complementary, we evaluate the required energy for duplication of information in the context of black hole complementarity by calculating the critical value of the rainbow parameter in the certain class of the rainbow Schwarzschild black hole. The resultant energy can be written as the well-defined limit for the vanishing rainbow parameter which characterizes the deformation of the relativistic dispersion relation in the freely falling frame. It shows that the duplication of information in quantum mechanics could not be allowed below a certain critical value of the rainbow parameter; however, it might be possible above the critical value of the rainbow parameter, so that the consistent formulation in our model requires additional constraints or any other resolutions for the latter case.