Thermal Fisher information for a rotating BTZ black hole

TL;DR

This paper extends the application of relativistic quantum metrology using Fisher information to rotating BTZ black holes, demonstrating sensitivity to black hole rotation and advancing quantum measurement techniques in curved spacetime.

Contribution

It introduces the use of Fisher information to detect black hole rotation, expanding previous static black hole studies to rotating cases in 2+1 dimensions.

Findings

Fisher information is sensitive to black hole rotation.

Quantum detectors can distinguish rotating from static black holes.

Extension of quantum metrology to rotating spacetime scenarios.

Abstract

Relativistic quantum metrology provides a framework within which we can quantify the quality of measurement and estimation procedures while accounting for both quantum and relativistic effects. The chief measure for describing such procedures is the Fisher information, which quantifies how sensitive a given estimation is to a variance of some underlying parameter. Recently, the Fisher information has been used to quantify the spacetime information accessible to two-level quantum particle detectors. We have previously shown that such a system is capable of discerning black hole mass for static black holes in 2+1 dimensions. Here, we extend these results to the astrophysically interesting case of rotating black holes and show that the Fisher information is also sensitive to the rotation of a black hole.