Relativistic tidal divergences in circular orbits and the dynamics of light rings

Abstract

Tidal forces acting on orbiting bodies arise from inhomogeneities in the gravitational field, generating stresses that can deform or even disrupt these objects. In this work, we analyze relativistic tidal forces associated with ultracompact objects described by static and spherically symmetric spacetimes, focusing on observers in circular geodesic motion. We show that, in contrast to the case of radial geodesics, tidal forces diverge as the orbit approaches null circular geodesics. As illustrative examples, we study two uniform-density stellar models: one isotropic and another supported purely by tangential stresses. We conjecture that the divergence of tidal forces near light rings may play a role in the nonlinear stability of ultracompact, horizonless objects.