Probing hidden topology with quantum detectors

TL;DR

This paper demonstrates that a quantum detector outside certain black holes can distinguish different interior topologies, revealing that quantum measurements can access information about the black hole's hidden structure.

Contribution

It shows that the transition rate of a static Unruh-DeWitt detector can detect differences in the interior topology of black holes, a novel way to probe hidden spacetime features.

Findings

Detector distinguishes between the two spacetimes at late times

Differences in isometries affect the detector's response

Quantum measurements can reveal interior topology information

Abstract

We consider the transition rate of a static Unruh-DeWitt detector in two $(2+1)$-dimensional black hole spacetimes that are isometric to the static Ba\~nados-Teitelboim-Zanelli black hole outside the horizon but have no asymptotically locally anti-de Sitter exterior behind the horizon. The spacetimes are the $\mathbb{R}\text{P}^{2}$ geon, with spatial topology $\mathbb{R}\text{P}^{2}\setminus\{\text{point at infinity}\}$, and the Swedish geon of \AA{}minneborg \emph{et al\/}, with spatial topology $T^{2}\setminus\{\text{point at infinity}\}$. For a conformal scalar field, prepared in the Hartle-Hawking-type state that is induced from the global vacuum on the anti-de Sitter covering space, we show numerically that the detector's transition rate distinguishes the two spacetimes, particularly at late exterior times, and we trace this phenomenon to the differences in the isometries that are broken by the quotient construction from the universal covering space. Our results provide an example in which information about the interior topology of a black hole is accessible to a quantum observer outside the black hole.