Local free-fall Temperature of modified Schwarzschild black hole in rainbow spacetime

TL;DR

This paper explores the local free-fall temperature of a modified Schwarzschild black hole within rainbow gravity, revealing finite temperature at the horizon for free-fall observers and divergence for stationary observers, with implications for black hole thermodynamics.

Contribution

It provides a (5+1)-dimensional flat embedding of the modified Schwarzschild black hole in rainbow gravity and analyzes the temperature behavior for different observer types.

Findings

Free-fall temperature is finite at the horizon for freely falling observers.

Fiducial observers measure divergent temperature at the horizon.

Temperatures satisfy relations similar to Schwarzschild black holes, modulated by rainbow functions.

Abstract

We obtain a (5+1)-dimensional global flat embedding of modified Schwarzschild black hole in rainbow gravity. We show that local free-fall temperature in rainbow gravity, which depends on different energy $\omega$ of a test particle, is finite at the event horizon for a freely falling observer, while local temperature is divergent at the event horizon for a fiducial observer. Moreover, these temperatures in rainbow gravity satisfy similar relations to those of the Schwarzschild black hole except overall factor $g(\omega)$, which plays a key role of rainbow functions in this embedding approach.