Some properties of accelerating observers in the Schwarzschild space

TL;DR

This paper explores the properties of accelerating observers in Schwarzschild spacetime, demonstrating their ability to detect radiation similar to the Unruh effect and proposing a general conjecture about null hypersurfaces and radiation detection.

Contribution

It introduces a method to construct accelerating observers in Schwarzschild space and shows they can detect radiation, extending the understanding of observer-dependent effects in curved spacetime.

Findings

Accelerating observers in Schwarzschild space can detect radiation analogous to the Unruh effect.

A special null hypersurface in Kruskal coordinates is used to define these observers.

Conjecture that observers near any null hypersurface can detect local radiation.

Abstract

It is well known that observers will be accelerated when they approach the planets. Thus, discussing the properties of accelerating observers in the Schwarzschild space is of sense. For the sake of simplicity, we can construct these observers' world lines by comparing with the observers in the Hawking effect and Unruh effect, whose world lines are both hyperbolic curves in the appropriate coordinates. We do it after defining a certain special null hypersurface in the Kruskal coordinates. Our result shows that these accelerating observers defined in our paper can also detect the radiation with the analogy of the Unruh effect, though locally. Furthermore, we conjecture that, for any null hypersurface in any spacetime, the corresponding observers who can at least locally detect the radiation from it can be found.