Trapping of null geodesics in slowly rotating spacetimes

TL;DR

This paper investigates how slow rotation in compact astrophysical objects affects the trapping of null geodesics, revealing that rotation influences trapping efficiency and can occur at larger radii than previously thought.

Contribution

It extends the study of null geodesic trapping from spherical symmetry to slowly rotating spacetimes using the Hartle-Thorne approximation, highlighting the effects of rotation.

Findings

Rotation causes differences in trapping efficiency for co-rotating and retrograde geodesics.

Trapping can occur at radii larger than 3GM/c^2 due to rotation.

Effective potentials and escape cones depend on the spacetime parameters.

Abstract

Extremely compact objects containing a region of trapped null geodesics could be of astrophysical relevance due to trapping of neutrinos with consequent impact on cooling processes or trapping of gravitational waves. These objects have previously been studied under the assumption of spherical symmetry. In the present paper, we consider a simple generalization by studying trapping of null geodesics in the framework of the Hartle-Thorne slow-rotation approximation taken to first order in the angular velocity, and considering a uniform-density object with uniform emissivity for the null geodesics. We calculate effective potentials and escape cones for the null geodesics and how they depend on the parameters of the spacetimes, and also calculate the "local" and "global" coefficients of efficiency for the trapping. We demonstrate that due to the rotation the trapping efficiency is different for co-rotating and retrograde null geodesics, and that trapping can occur even for $R>3GM/c^2$, contrary to what happens in the absence of rotation.