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.
Highlights
Higher-dimensional black holes have played an important role in understanding basic properties of fundamental theories, such as string theory
We show analytically that the radius of an innermost stable circular orbit monotonically depends on the size of an extra dimension
We have shown the existence of the stable circular orbits for massive particles around the static squashed Kaluza-Klein black holes with a single horizon and two horizons in the five-dimensional Einstein-Maxwell theory, reducing the geodesic motion of particles to a two-dimensional potential problem
Summary
Higher-dimensional black holes have played an important role in understanding basic properties of fundamental theories, such as string theory. It is of great interest to consider higher-dimensional Kaluza-Klein black hole spacetimes, which look like four-dimensional ones at least at large distances The studies on such Kaluza-Klein black holes may help us to get some insights into the major open problem of how to compactify and stabilize extra dimensions in string theory. We study the motion of massive particles around a squashed Kaluza-Klein black hole with a compactified extra-dimensional space where a black hole extends. We consider motion of particles as a two-dimensional potential problem, focusing on the static charged black hole solutions with a single horizon and two horizons in the five-dimensional EinsteinMaxwell theory, which were constructed in Ref.
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