Stable circular orbits in caged black hole spacetimes

TL;DR

This paper investigates the existence and stability of circular orbits around a five-dimensional caged black hole, revealing how extra-dimensional size influences orbital properties and stability.

Contribution

It demonstrates the existence and stability of circular orbits in caged black hole spacetimes and analyzes their dependence on extra-dimensional size.

Findings

Stable circular orbits exist in the asymptotic region.

No stable orbits near the black hole due to compactification effects.

The size of extra dimensions affects the innermost stable orbit.

Abstract

We consider the motion of massive and massless particles in a five-dimensional spacetime with a compactified extra-dimensional space where a black hole is localized, i.e., a caged black hole spacetime. We show the existence of circular orbits and reveal their sequences and stability. In the asymptotic region, stable circular orbits always exist, which implies that four-dimensional gravity is more dominant because of the small extra-dimensional space. In the vicinity of a black hole, they do not exist because the effect of compactification is no longer effective. We also clarify the dependence of the sequences of circular orbits on the size of the extra-dimensional space by determining the appearance of the innermost stable circular orbit and the last circular orbit (i.e., the unstable photon circular orbit).