A Fast New Public Code for Computing Photon Orbits in a Kerr Spacetime

Abstract

Relativistic radiative transfer problems require the calculation of photon trajectories in curved spacetime. We present a novel technique for rapid and accurate calculation of null geodesics in the Kerr metric. The equations of motion from the Hamilton-Jacobi equation are reduced directly to Carlson's elliptic integrals, simplifying algebraic manipulations and allowing all coordinates to be computed semi-analytically for the first time. We discuss the method, its implementation in a freely available FORTRAN code, and its application to toy problems from the literature.

15 pages, 10 figures, accepted by ApJ

References in corpus (10)

• Multi-Temperature Blackbody Spectrum of a Thin Accretion Disk around a Kerr Black Hole: Model Computations and Comparison with Observations
• Simulating the Emission and Outflows from Accretion Disks
• Extreme Gravitational Lensing near Rotating Black Holes
• Frequency-Dependent Shift in the Image Centroid of the Black Hole at the Galactic Center as a Test of General Relativity
• Light Curves from an MHD Simulation of a Black Hole Accretion Disk
• Radiation Transfer of Emission Lines in Curved Space-Time
• Optical caustics of Kerr spacetime: the full structure
• Iron line profiles and self-shadowing from relativistic thick accretion discs
• Radiative Transfer Along Rays in Curved Spacetimes
• Limits on the Position Wander of Sgr A*

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