Is the equivalence for the response of static scalar sources in the Schwarzschild and Rindler spacetimes valid only in four dimensions?

TL;DR

This paper investigates whether the known equivalence of responses for static scalar sources in Schwarzschild and Rindler spacetimes extends beyond four dimensions, concluding that it does not in higher dimensions.

Contribution

The paper demonstrates that the equivalence between responses in Schwarzschild and Rindler spacetimes, valid in four dimensions, fails in higher-dimensional spacetimes.

Findings

Equivalence holds only in four dimensions.

Higher dimensions break the response equivalence.

Results highlight dimensional dependence of scalar field responses.

Abstract

It was shown recently that in four dimensions scalar sources with fixed proper acceleration minimally coupled to a massless Klein-Gordon field lead to the same responses when they are (i) uniformly accelerated in Minkowski spacetime (in the inertial vacuum) and (ii) static in the Schwarzschild spacetime (in the Unruh vacuum). Here we show that this equivalence is broken if the spacetime dimension is more than four.