Geodesic circular orbits sharing the same orbital frequencies in the black string spacetime

TL;DR

This paper investigates how an extra compact spatial dimension in black string spacetime affects the pairing of geodesic orbits sharing the same orbital frequencies, revealing increased pairing and a critical limit for such orbits.

Contribution

It introduces the concept of isofrequency pairing in black string spacetime and analyzes the influence of the extra dimension on these geodesic orbits, highlighting new phenomena.

Findings

Extra dimension increases the number of isofrequency pairings.

Isofrequency pairing cannot occur beyond a critical conserved quantity value.

Orbits form in a cylindrical manner due to the extra dimension.

Abstract

Here we consider isofrequency pairing of geodesic orbits that share the same three orbital frequencies associated with $\Omega^{\hat{r}}$, $\Omega^{\hat{\varphi}}$, and $\Omega^{\hat{\omega}}$ in a particular region of parameter space around black string spacetime geometry. We study the effect arising from the extra compact spatial dimension on the isofrequency pairing of geodesic orbits and show that such orbits would occur and become in a cylindrical manner in the allowed region as particles move along the black string. We find that the effect due to the extra dimension leads to an increase in the number of the isofrequency pairing of geodesic orbits. We also find that isofrequency pairing of geodesic orbits in the region of parameter space can not be realized beyond the critical value $J_{cr} \approx 0.096$ of the conserved quantity of the motion due to the extra compact spatial dimension for given parameters of the black string.