Periodic orbits around brane-world black holes

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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q<0$$\end{document} in the DMPR brane-world black holes have higher energy in comparison to the ones with Q>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Q>0$$\end{document} 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.