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An asymptotically consistent approximant for the equatorial bending angle of light due to Kerr black holes
By Nathaniel S. Barlow Steven J. Weinstein Joshua A. Faber
Published in Classical and Quantum Gravity 34, 135017(Monday, January 23, 2017)

Abstract

An accurate closed-form expression is provided to predict the bending angle of light as a function of impact parameter for equatorial orbits around Kerr black holes of arbitrary spin. This expression is constructed by assuring that the weak- and strong-deflection limits are explicitly satisfied while maintaining accuracy at intermediate values of impact parameter via the method of asymptotic approximants (Barlow et al, 2016 Q.~J.~Mech.~Appl.~Math., doi=10.1093/qjmam/hbw014).  To this end, the strong deflection limit for a prograde orbit around an extremal  black hole is examined, and the full non-vanishing asymptotic behavior is determined.  The derived approximant may be an attractive alternative to computationally expensive elliptical integrals used in black hole simulations.  

CCRG Authors

Faber, Joshua