GEMS embeddings of Hayward regular black holes in massless and massive gravities

TL;DR

This paper constructs higher-dimensional embeddings of Hayward regular black holes in both massless and massive gravities, analyzing temperature effects and confirming the equivalence of Unruh and Hawking temperatures in these models.

Contribution

It introduces new embeddings of Hayward black holes in higher-dimensional spacetimes within massless and massive gravity frameworks, and compares temperature effects for different observers.

Findings

Unruh temperatures match Hawking temperatures for embedded black holes.

Freely falling temperatures remain finite at the horizon.

Embedding coordinates enable temperature comparisons in different gravity models.

Abstract

After finding a solution for the Hayward regular black hole (HRBH) in massive gravity, we embed the (3+1)-dimensional HRBHs both in massless and in massive gravities into (5+2)- and (6+3)-dimensional Minkowski spacetimes, respectively. Here, massive gravity denotes that a graviton acquires a mass holographically by broken momentum conservation in the HRBH. The original HRBH has no holographically added gravitons, which we call massless. Making use of newly found embedding coordinates, we obtain desired Unruh temperatures and compare them with the Hawking and local fiducial temperatures, showing that the Unruh effect for a uniformly accelerated observer in a higher dimensional flat spacetime is equal to the Hawking effect for a fiducial observer in a black hole spacetime. We also obtain freely falling temperatures of the HRBHs in massless and massive gravities seen by freely falling observers, which remain finite even at the event horizons while becoming the Hawking temperatures in asymptotic infinity.