# Thermal Fisher Information for a Rotating BTZ Black Hole

## TL;DR

This paper explores how quantum measurements can detect properties of rotating black holes using Fisher information.

## Contribution

The study extends the use of Fisher information to detect rotation in black holes, beyond previous work on static black holes.

## Key findings

- Fisher information can discern the rotation parameter of a black hole.
- Quantum particle detectors can access spacetime information related to black hole rotation.
- The method is applicable to rotating BTZ black holes in 2+1 dimensions.

## 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 in 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.