Rainbow Rindler metric and Unruh effect

TL;DR

This paper derives the rainbow-Rindler metric from first principles, linking it with the Unruh effect and rainbow black hole thermodynamics, thereby advancing the understanding of energy-dependent spacetime modifications.

Contribution

It provides the first explicit derivation of the rainbow-Rindler metric and connects the Unruh temperature with rainbow black hole temperature, filling a gap in rainbow gravity research.

Findings

Derived explicit coordinate transformations for rainbow Minkowski to accelerated frames.

Obtained the rainbow-Rindler metric with properly identified parameters.

Found that the Unruh temperature matches the rainbow black hole temperature.

Abstract

The energy of a particle moving on a spacetime, in principle, can affect the background metric. The modifications to it depend on the ratio of energy of the particle and the Planck energy, known as rainbow gravity. Here we find the explicit expressions for the coordinate transformations from rainbow Minkowski spacetime to accelerated frame. The corresponding metric is also obtained which we call as rainbow-Rindler metric. So far we are aware of, no body has done it in a concrete manner. Here this is found from the first principle and hence all the parameters are properly identified. The advantage of this is that the calculated Unruh temperature is compatible with the Hawking temperature of the rainbow black hole horizon, obtained earlier. Since the accelerated frame has several importance in revealing various properties of gravity, we believe that the present result will not only fill that gap, but also help to explore different aspects of rainbow gravity paradigm.