Mapping Hawking temperature in the spinning constant curvature black hole spaces into Unruh temperature

TL;DR

This paper demonstrates the equivalence between Hawking and Unruh temperatures in higher-dimensional spinning black hole spacetimes using a global embedding approach, linking curved spacetime thermodynamics to flat space acceleration.

Contribution

It establishes a novel connection between Hawking and Unruh temperatures in 5D spinning black holes with constant curvature through a global embedding method.

Findings

Hawking temperature at finite distances matches Unruh temperature in flat embedding space.

The equivalence holds for both positive and negative constant curvature black holes.

The approach provides a new perspective on black hole thermodynamics in higher dimensions.

Abstract

We established the equivalence between the local Hawking temperature measured by the time-like Killing observer located at some positions $r$ with finite distances from the outer horizon $r_+$ in the 5-dimensional spinning black hole space with both negative and positive constant curvature, and the Unruh temperature measured by the Rindler observer with constant acceleration in the 6-dimensional flat space by employing the globally embedding approach.