# Over the horizon: distinguishing the Schwarzschild spacetime and the $\mathbb{RP}^3$ spacetime using an Unruh-DeWitt detector

## TL;DR

This paper demonstrates that an Unruh-DeWitt detector can differentiate between the Schwarzschild spacetime and the $ ext{RP}^3$ geon, revealing non-local topological information beyond the event horizon through detector responses.

## Contribution

It introduces a novel method for using particle detectors to identify topological differences in spacetimes that are classically indistinguishable outside the horizon.

## Key findings

- Detector responses vary between $ ext{RP}^3$ geon and Schwarzschild spacetime.
- Transition dependence on detector gap provides a potential observational signal.
- Non-local topological features influence local detector measurements.

## Abstract

We show that a particle detector can distinguish the $\mathbb{RP}^3$ geon from the Schwarzschild black hole, even though they differ only by a topological identification beyond the event horizon. This shows that the detector can read out information about the non-local structure even when separated from the non-locality by an event horizon. Our analysis of the dependence of the transition on the detector gap is novel, and in principle presents an interesting observational signal.