Equatorial timelike circular orbits around generic ultracompact objects

TL;DR

This paper demonstrates that the structure of equatorial timelike circular orbits around ultracompact objects is determined solely by the radial stability of light-rings, with implications for exotic stars and black holes, including energy efficiency.

Contribution

It establishes a direct link between light-ring stability and the stability of circular orbits around ultracompact objects, extending understanding beyond Kerr black holes.

Findings

Unstable light-rings bound regions of unstable or no TCOs.

Stable light-rings bound regions of stable TCOs.

Efficiencies exceeding 42% are achievable around certain ultracompact objects.

Abstract

For a stationary, axisymmetric, asymptotically flat, ultra-compact [$i.e.$ containing light-rings (LRs)] object, with a $\mathbb{Z}_2$ north-south symmetry fixing an equatorial plane, we establish that the structure of timelike circular orbits (TCOs) in the vicinity of the equatorial LRs, for either rotation direction, depends exclusively on the radial stability of the LRs. Thus, an unstable LR delimits a region of unstable TCOs (no TCOs) radially above (below) it; a stable LR delimits a region of stable TCOs (no TCOs) radially below (above) it. Corollaries are discussed for both horizonless ultra-compact objects and black holes. We illustrate these results with a variety of exotic stars examples and non-Kerr black holes, for which we also compute the efficiency associated with converting gravitational energy into radiation by a material particle falling under an adiabatic sequence of TCOs. For most objects studied, it is possible to obtain efficiencies larger than the maximal efficiency of Kerr black holes, $i.e.$ larger than $42\%$.