Analysis of minimum orbital periods around d-dimensional charged black holes

TL;DR

The paper addresses bounds on the minimum orbital period for test objects around $d$-dimensional charged black holes in asymptotically flat spacetimes. It derives the equatorial circular-orbit Period $T(r)$ from the metric, locates the minimum via $dT/dr=0$, and provides a closed-form expression for the minimum period, showing it decreases with charge. Analytically, it establishes dimension-dependent upper and lower bounds on $T_{min}$, with a real-valuedness constraint on the charge; the bounds scale as $M^{1/(d-3)}$ and reproduce known results in $d=4$ and $d=5$. These results generalize previous limits and offer constraints for gravity theories in higher dimensions.

Abstract

This paper investigates the bounds on the minimum orbital period for test objects around d-dimensional charged black holes in asymptotically flat spacetimes. We find numerically that the minimum orbital period decreases as the charge of the black hole increases. Thus, the upper limit is reached for an uncharged black hole, while the lower limit is attained for a maximally charged one. We then analytically derive the upper and lower bounds for the minimum orbital period. These results improve our understanding of dynamics around d-dimensional black holes and impose constraints on candidate gravity theories.