Periodic equatorial orbits in a black bounce scenario

TL;DR

This paper investigates equatorial periodic orbits in a black bounce model, revealing how internal structure variations can cause observable differences, and extends existing classification schemes to wormholes and black holes.

Contribution

It extends the classification of equatorial orbits to black bounce models and wormholes, showing how small parameter changes significantly affect orbital dynamics.

Findings

Orbits can be characterized by a triplet of integers similar to Schwarzschild and Kerr.

The classification scheme applies to wormholes with minor modifications.

Small changes in the black bounce parameter can lead to notable orbital differences.

Abstract

We study equatorial closed orbits in a popular black bounce model to see if the internal structure of these objects could lead to peculiar observable features. Paralleling the analysis of the Schwarzschild and Kerr metrics, we show that in the black bounce case each orbit can also be associated with a triplet of integers which can then be used to construct a rational number characterizing each periodic orbit. When the black bounce solution represents a traversable wormhole, we show that the previous classification scheme is still applicable with minor adaptations. We confirm in this way that this established framework enables a complete description of the equatorial dynamics across a spectrum of cases, from regular black holes to wormholes. Varying the black bounce parameter $r_{min}$, we compare the trajectories in the Simpson-Visser model with those in the Schwarzschild metric (and the rotating case with Kerr). We find that in some cases even small increments in $r_{min}$ can lead to significant changes in the orbits.