Static stable timelike circular orbits and Aschenbach effect in horizonless solutions of Einsteinian cubic gravity

Abstract

In modified gravity theories, horizonless compact objects serve as a compelling alternative to black holes for testing strong-field gravity. Einsteinian cubic gravity (ECG) provides a gravitational framework for constructing these viable astrophysical models. We investigate the existence, stability, and observable signatures of static stable timelike circular orbits (SSTCOs) in static spherically symmetric ECG horizonless spacetimes. We derive timelike geodesic equations, construct the effective potential for circular orbits, and perform a numerical integration to verify orbital stability. We confirm that SSTCOs exist in both solution branches of ECG horizonless objects and that their radii coincide with the innermost stable circular orbit (ISCO). The Aschenbach effect manifests as a non-monotonic radial dependence of a zero angular momentum observer (ZAMO) measured velocity. Furthermore, we find that the stability of circular orbits exhibits a 'double stable region' structure. As the specific energy $E$ of a test particle transitions from the outer edge to the inner edge (i.e., the ISCO) of the inner stable region, its variation can exceed $1$ (i.e., $\hat{I}”E>1$), implying that during this process, the gravitational system can release an amount of energy exceeding the rest mass of the particle itself.

16 pages, 10 figures. Added a discussion on the oscillatory frequency distribution