Magnification relations for Kerr lensing and testing cosmic censorship
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 postNewtonian order. We show that there are postNewtonian 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 nearfuture 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 postNewtonian order. A simple physical explanation for this degeneracy is also given.
 Publication:

Physical Review D
 Pub Date:
 September 2007
 DOI:
 10.1103/PhysRevD.76.064024
 arXiv:
 arXiv:0706.0132
 Bibcode:
 2007PhRvD..76f4024W
 Keywords:

 04.70.Bw;
 04.25.Nx;
 95.30.Sf;
 98.62.Sb;
 Classical black holes;
 PostNewtonian approximation;
 perturbation theory;
 related approximations;
 Relativity and gravitation;
 Gravitational lenses and luminous arcs;
 General Relativity and Quantum Cosmology;
 Astrophysics
 EPrint:
 13 pages, version 2: references added, minor changes. To appear in Phys. Rev. D