Magnification relations for Kerr lensing and testing Cosmic Censorship

TL;DR

This paper investigates gravitational lensing by Kerr black holes, deriving post-Newtonian corrections to magnification relations, and proposes new observables to measure black hole spin, providing a potential test for the Cosmic Censorship conjecture.

Contribution

It introduces post-Newtonian corrections to Kerr lensing magnification relations and proposes new observables to measure the black hole's spin parameter a/m.

Findings

Post-Newtonian corrections to magnification sums and centroid depend on a/m.

New lensing observables can measure black hole spin with current or near-future technology.

Potential to test the Cosmic Censorship conjecture using gravitational lensing data.

Abstract

A Kerr black hole with mass parameter m and angular momentum parameter a acting as a gravitational lens gives rise to two images in the weak field limit. We study the corresponding magnification relations, namely the signed and absolute magnification sums and the centroid up to post-Newtonian order. We show that there are post-Newtonian corrections to the total absolute magnification and centroid proportional to a/m, which is in contrast to the spherically symmetric case where such corrections vanish. Hence we also propose a new set of lensing observables for the two images involving these corrections, which should allow measuring a/m with gravitational lensing. In fact, the resolution capabilities needed to observe this for the Galactic black hole should in principle be accessible to current and near-future instrumentation. Since a/m >1 indicates a naked singularity, a most interesting application would be a test of the Cosmic Censorship conjecture. The technique used to derive the image properties is based on the degeneracy of the Kerr lens and a suitably displaced Schwarzschild lens at post-Newtonian order. A simple physical explanation for this degeneracy is also given.