Stable circular orbits in Kaluza-Klein black hole spacetimes

TL;DR

This paper analyzes the stability of circular particle orbits around Kaluza-Klein black holes, revealing how extra dimensions and black hole separation influence orbit stability and radius.

Contribution

It provides an analytical study of stable circular orbits in five-dimensional Kaluza-Klein black hole spacetimes, highlighting the effects of extra dimensions and black hole separation.

Findings

Stable circular orbits exist around squashed Kaluza-Klein black holes.

The innermost stable orbit radius depends on extra dimension size and black hole separation.

Orbit stability patterns change with black hole separation and extra dimension size.

Abstract

Reducing motion of particles to a two-dimensional potential problem, we show that there are stable circular orbits around a squashed Kaluza-Klein black hole with a spherical horizon and multi-Kaluza-Klein black holes with two spherical horizons in five dimensions. For a single horizon, we show analytically that the radius of an innermost stable circular orbit monotonically depends on the size of an extra dimension. For two horizons, the radius of an innermost stable circular orbit depends on the separation between two black holes besides the size of an extra dimension. More precisely, the set of the stationary points of the potential is composed of two branches. For a large separation, stable circular orbits exist on the two branches regardless of the size of an extra dimension, and in particular, on one branch, the set of stable circular orbits is connected for the small extra dimension but has two disconnected parts for the large extra dimension. For a small separation, only on one branch it exists, and the radius of an innermost stable circular orbit monotonically increases with an extra-dimension size.