Abstract
A black hole on a three-brane in five-dimensional spacetime was predicted by Dadhich, Maartens, Papadopoulos and Rezania (DMPR). In order to reveal some signatures for observations, we investigate a timelike particle’s motion around the DMPR brane-world black holes. We find that, both in the innermost stable circular orbits (ISCO) and the marginally bound orbits (MBO), the particle’s angular momentum and its radius decrease with the increase of Q, where Q is a tidal charge parameter and may be negative and positive in the brane-world black holes. From these results, the corresponding periodic orbits with different energy levels are analyzed numerically by employing a taxonomy, which is related to the adiabatic inspiral regime in the gravitational wave radiation. It clearly shows that a rational number defined by the taxonomy increases with the particle’s energy. In addition, periodic orbits with Q<0 in the DMPR brane-world black holes have higher energy in comparison to the ones with Q>0 and in the Schwarzschild black holes. Our results might provide hints for distinguishing the DMPR brane-world black holes from other black holes by the timelike particle’s periodic orbits in the future.
Highlights
Strong gravitational field could be well investigated by using a test particle’s orbits around black holes
During the adiabatic inspiral regime, a series of periodic orbits serves as a continuing transitional orbit and play a significance role in the research of the gravitational wave radiation [19]
A taxonomy of periodic orbits for a timelike particle around black holes has been recently proposed in Ref. [21]
Summary
In the detection of gravitational waves, for example, an extreme mass ratio inspiral is formed from one stellar mass black hole whirling closely around a supermassive one. During the adiabatic inspiral regime, a series of periodic orbits serves as a continuing transitional orbit and play a significance role in the research of the gravitational wave radiation [19] Given this fact, a taxonomy of periodic orbits for a timelike particle around black holes has been recently proposed in Ref. By using a delta function rather than a confining potential in the energy-momentum tensor, Dadhich, Maartens, Papadopoulos and Rezania (DMPR) [38] predicted exact solutions for static black holes localized on a three-brane in five-dimensional gravity in the RandallSundrum scenario. In view of the unique feature of the taxonomy, in this work, periodic orbits of a timelike particle around the DMPR brane-world black holes will be investigated.
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