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.

Dadhich，Maartens，Papadopoulos和Rezania（DMPR）预测了五维时空中三脑的黑洞。为了揭示观察的特征，我们研究了DMPR大脑世界黑洞周围类似时间的粒子运动。我们发现，在最内层的稳定圆形轨道（ISCO）和边际约束轨道（MBO）中，粒子的角动量及其半径都随着Q的增加而减小，其中Q是潮汐电荷参数，在Brane-world黑洞中可能为负也可能为正。根据这些结果，通过采用与重力波辐射中的绝热吸气形式有关的分类法，对具有不同能级的相应周期性轨道进行了数值分析。它清楚地表明，由分类法定义的有理数随粒子的能量而增加。此外，与具有\（Q> 0 \）和Schwarzschild黑洞的轨道相比，在DMPR麸质世界黑洞中具有\（Q <0 \）的周期性轨道具有更高的能量。我们的结果可能为将来通过类似时间的粒子的周期性轨道将DMPR谱系世界黑洞与其他黑洞区分开提供提示。