Note on uncertainty relations in doubly special relativity and rainbow gravity

TL;DR

This paper introduces modified commutation relations in doubly special relativity and rainbow gravity frameworks, demonstrating their compatibility with Hawking temperature calculations for rainbow Schwarzschild black holes.

Contribution

It proposes new commutation relations dependent on rainbow functions, enhancing the theoretical consistency of Hawking temperature calculations in rainbow gravity.

Findings

Modified commutation relations depend on rainbow functions

Compatibility with Hawking temperature calculations

Potential implications for black hole thermodynamics

Abstract

We present commutation relations depending on the rainbow functions which are slightly different from the well-known results. However, the advantage of these new commutation relations are compatible with the calculation of the Hawking temperature in the rainbow Schwarzschild black hole.