A Morse-theoretical analysis of gravitational lensing by a Kerr-Newman black hole

TL;DR

This paper uses Morse theory to analyze gravitational lensing by Kerr-Newman black holes, showing infinitely many lightlike geodesics and images are possible under certain conditions, linked to force reversal phenomena.

Contribution

It provides a Morse-theoretical framework for understanding multiple images in Kerr-Newman spacetime, revealing the connection to force reversal effects.

Findings

Infinitely many lightlike geodesics exist under specified conditions.

All geodesics from an event to a worldline are confined to a spherical shell.

Infinite images are linked to centrifugal-plus-Coriolis force reversal.

Abstract

Consider, in the domain of outer communication of a Kerr-Newman black hole, a point (observation event) and a timelike curve (worldline of light source). Assume that the worldline of the source (i) has no past end-point, (ii) does not intersect the caustic of the past light-cone of the observation event, and (iii) goes neither to the horizon nor to infinity in the past. We prove that then for infinitely many positive integers k there is a past-pointing lightlike geodesic of (Morse) index k from the observation event to the worldline of the source, hence an observer at the observation event sees infinitely many images of the source. Moreover, we demonstrate that all lightlike geodesics from an event to a timelike curve in the domain of outer communication are confined to a certain spherical shell. Our characterization of this spherical shell shows that in the Kerr-Newman spacetime the occurrence of infinitely many images is intimately related to the occurrence of centrifugal-plus-Coriolis force reversal.