Mapping Hawking into Unruh for global embeddings

TL;DR

This paper investigates the conditions under which the Hawking into Unruh mapping via global embeddings into Minkowski spacetime is valid, revealing constraints and differences in potential barriers that affect the interpretation of Hawking and Unruh effects.

Contribution

It identifies a specific constraint on extrinsic acceleration for GEMS embeddings and analyzes potential barriers, clarifying limitations of the Hawking-Unruh mapping approach.

Findings

A constraint on extrinsic acceleration is necessary for GEMS Hawking-Unruh mapping.

Potential barriers are finite at infinity, allowing detection of Unruh radiation.

Differences in potential barriers indicate GEMS approach is not fully complete.

Abstract

We study the mechanism of global embeddings into the Minkowski spacetime(GEMS) with the Hawking into Unruh mapping. We find a constraint that the extrinsic acceleration of the static observer in the Riemann space must satisfy for such embeddings. Thus the question raised by Paston in Ref.\cite{1}, that is, when does the Hawking into Unruh mapping for global embeddings work, is partly addressed. We also calculate the potential barrier of a scalar field to reach r $\rightarrow\infty$ in the ambient space. The results show that the potential barrier is finite, hence the static observer at r $\rightarrow\infty$ can indeed detect the radiation caused by the Unruh effect from the embedding view. However the potential barriers calculated in both the Riemann background and the Minkowski background are not coincident, therefore the GEMS approach is not complete and the Hawking effect can be distinguished from the Unruh effect of the GEMS in principle.