# Gyroscope precession frequency analysis of a five dimensional charged rotating Kaluza-Klein black hole

## TL;DR

This paper analyzes the spin precession frequency of a gyroscope around a five-dimensional rotating Kaluza-Klein black hole, identifying divergence regions and comparing static and rotating cases to distinguish it from Kerr-Newman black holes.

## Contribution

It derives conditions for gyroscope motion and precession divergence in five-dimensional Kaluza-Klein black holes, and proposes mass-independent schemes to differentiate these from Kerr-Newman black holes.

## Key findings

- Precession frequency diverges at two locations outside the horizon.
- Static case resembles Schwarzschild black hole behavior.
- Proposes methods to distinguish KK black holes from Kerr-Newman black holes.

## Abstract

In this paper, we study the spin precession frequency of a test gyroscope attached to a stationary observer in the five dimensional rotating Kaluza-Klein black hole (RKKBH). We derive the conditions under which the test gyroscope moves along a timelike trajectory in this geometry and the regions where the spin precession frequency diverges. The magnitude of the gyroscope precession frequency around KK black hole diverges at two spatial locations outside the event horizon. However in the static case, the behavior of the Lense Thirring frequency of a gyroscope around KK black hole is much like an ordinary Schwarzschild black hole. Since a rotating Kaluza-Klein black hole is a generalization of Kerr-Newman black hole, we present two mass-independent schemes to distinguish these two spacetimes.