Gravitational lensing in spherically symmetric static spacetimes with centrifugal force reversal

TL;DR

This paper demonstrates that in any spherically symmetric static spacetime, the properties of the photon sphere, centrifugal force reversal, and lensing limits are fundamentally interconnected, extending known Schwarzschild results.

Contribution

It proves a general theorem linking key properties of photon spheres, centrifugal force, and lensing in all spherically symmetric static spacetimes, beyond Schwarzschild.

Findings

The photon sphere, centrifugal force reversal, and lensing limits are equivalent properties in these spacetimes.

Examples include black holes and wormholes illustrating the theorem.

The results unify understanding of gravitational lensing phenomena across different spacetimes.

Abstract

In Schwarzschild spacetime the value $r=3m$ of the radius coordinate is characterized by three different properties: (a) there is a ``light sphere'', (b) there is ``centrifugal force reversal'', (c) it is the upper limiting radius for a non-transparent Schwarschild source to act as a gravitational lens that produces infinitely many images. In this paper we prove a theorem to the effect that these three properties are intimately related in {\em any} spherically symmetric static spacetime. We illustrate the general results with some examples including black-hole spacetimes and Morris-Thorne wormholes.