Nondivergent deflection of light around a photon sphere of a compact object

TL;DR

This paper shows that stable photon spheres in certain spacetimes cause nondivergent light deflection, contrasting with the divergent behavior near unstable photon spheres, and explores implications for gravitational lensing.

Contribution

It reveals that stable photon spheres lead to finite, nondivergent light deflection, challenging the common understanding of divergence near photon spheres in black hole spacetimes.

Findings

Stable photon spheres do not cause divergent light deflection.

Nondivergent deflection depends on source and receiver distances.

Weyl gravity solutions exemplify nondivergent deflection near stable PS.

Abstract

We demonstrate that the location of a stable photon sphere (PS) in a compact object is not always an edge such as the inner boundary of a black hole shadow, whereas the location of an unstable PS is known to be the shadow edge notably in the Schwarzschild black hole. If a static spherically symmetric (SSS) spacetime has the stable outermost PS, the spacetime cannot be asymptotically flat. A nondivergent deflection is caused for a photon traveling around a stable PS, though a logarithmic divergent behavior is known to appear in most of SSS compact objects with an unstable photon sphere. The reason for the nondivergence is that the closest approach of a photon is prohibited in the immediate vicinity of the stable PS when the photon is emitted from a source (or reaches a receiver) distant from a lens object. The finite gap size depends on the receiver and source distances from the lens as well as the lens parameters. The mild deflection angle of light can be approximated by an arcsine function. A class of SSS solutions in Weyl gravity exemplify the nondivergent deflection near the stable outer PS.