Accurate closed-form trajectories of light around a Kerr black hole using asymptotic approximants

Abstract

Highly accurate closed-form expressions that describe the full trajectory of photons propagating in the equatorial plane of a Kerr black hole are obtained using asymptotic approximants. This work extends a prior study of the overall bending angle for photons (Barlow, et al. 2017, Class. Quantum Grav., 34, 135017). The expressions obtained provide accurate trajectory predictions for arbitrary spin and impact parameters, and provide significant time advantages compared with numerical evaluation of the elliptic integrals that describe photon trajectories. To construct approximants, asymptotic expansions for photon deflection are required in various limits. To this end, complete expansions are derived for the azimuthal angle as a function of radial distance from the black hole in the far-distance and closest-approach (pericenter) limits, and new coefficients are reported for the bending angle in the weak-field limit (large impact parameter).

29 pages, 11 figures

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Cited by in corpus (4)

• Equatorial light bending around Kerr-Newman black holes
• On the use of asymptotically motivated gauge functions to obtain convergent series solutions to nonlinear ODEs
• Analysis of scalar fields with series convolution
• Measuring black hole spin through gravitational lensing of pulsars