Photon escape cones, physical and optical metrics, asymptotic and near-horizon physics

TL;DR

This paper analyzes photon escape cones in static spherically symmetric spacetimes, exploring their relation to optical metrics, photon spheres, and near-horizon physics, with applications to black holes and wormholes.

Contribution

It reveals that photon spheres correspond to wormhole throats in the optical metric and links escape cone solid angles to physical and optical properties, including surface gravity.

Findings

Photon spheres are wormhole throats in the optical metric.

Escape cone solid angle relates to capture cross section and metric properties.

Near-horizon escape cones connect to surface gravity.

Abstract

We consider the explicit analytic behaviour of photon escape cones in generic static spherically symmetric spacetimes, emphasizing the interplay between the physical spacetime metric and the optical metric, and the interplay between large-distance asymptotic and near-horizon physics. The circular photon orbits (photon spheres) are shown to be given by wormhole throats in the optical metric, (not the physical metric), and the escape cone solid angle is easily calculable in terms of the capture cross section, sigma_{capture}, the area of the spherical 2-surfaces, and the norm of the timelike Killing vector. Under appropriate circumstances, for near-horizon photon emission the escape cone solid angle can be related to the surface gravity kappa_H. We provide a number of illustrative examples, involving both black holes and wormholes, including situations with multiple photon spheres.