Abstract
In higher-dimensional Schwarzschild black hole spacetimes, there are no stable bound orbits of particles. In contrast to this, it is shown that there are stable bound orbits in a five-dimensional black lens spacetime.
Highlights
It is an issue of physical interest whether a black hole spacetime has bound orbits of particles
The centrifugal force and gravitational force make a local minimum of the potential corresponding to a stable circular orbit, whereas for the higher dimensions, the effective potential has no local minimum because near the event horizon the gravitational potential becomes more dominated than for four dimensions
The exact solutions were found in five-dimensional Einstein theory [5,6] and fivedimensional minimal supergravity [7]
Summary
It is an issue of physical interest whether a black hole spacetime has bound orbits of particles. The centrifugal force and gravitational force make a local minimum of the potential corresponding to a stable circular orbit, whereas for the higher dimensions, the effective potential has no local minimum because near the event horizon the gravitational potential becomes more dominated than for four dimensions. For the lens space topologies, the supersymmetric solutions with the horizon topologies of Lðn; 1Þ were first constructed in the five-dimensional minimal supergravity [20,21]. Because it seems that the black lens cannot admit the separability of the geodesic equations, we cannot show the existence/nonexistence of stable bound orbits by merely solving a one-dimensional potential problem in the radial direction.
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