An asymptotically consistent approximant for the equatorial bending angle of light due to Kerr black holes

Authors: 
Nathaniel S. Barlow Steven J. Weinstein Joshua A. Faber
Journal: 
CQG, submitted
Volume: 
Page number: 
Publication date: 
January 23, 2017
E-print ID: 
1701.05828

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.  

 

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