The Null Geodesics of the Kerr Exterior

Abstract

The null geodesic equation in the Kerr spacetime can be expressed as a set of integral equations involving certain potentials. We classify the roots of these potentials and express the integrals in manifestly real Legendre elliptic form. We then solve the equations using Jacobi elliptic functions, providing the complete set of null geodesics of the Kerr exterior as explicit parameterized curves.

arXiv comment24 pages, 4 figures. v2: minor edits, matches published version. v3: corrected errors found after publication

References in corpus (8)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• Perturbative Approach to an orbital evolution around a Supermassive black hole
• Lensing by Kerr Black Holes
• A Fast New Public Code for Computing Photon Orbits in a Kerr Spacetime
• Analytical solutions of bound timelike geodesic orbits in Kerr spacetime
• Rotating black hole orbit functionals in the frequency domain
• Observational Signature of High Spin at the Event Horizon Telescope
• Particle motion near high-spin black holes

Cited by in corpus (87)

• The Shape of the Black Hole Photon Ring: A Precise Test of Strong-Field General Relativity
• Lensing by Kerr Black Holes
• Observing the Inner Shadow of a Black Hole: A Direct View of the Event Horizon
• Spherical orbits around a Kerr black hole
• Images and photon ring signatures of thick disks around black holes
• Orbital motion near Sagittarius A* -- Constraints from polarimetric ALMA observations
• The Polarized Image of a Synchrotron Emitting Ring of Gas Orbiting a Black Hole
• Photon Ring Autocorrelations
• Polarized Image of Equatorial Emission in the Kerr Geometry
• On the Observable Shape of Black Hole Photon Rings
• Strong gravitational lensing by Kerr and Kerr-Newman black holes
• From a locality-principle for new physics to image features of regular spinning black holes with disks
• Revisiting the shadow of braneworld black holes
• Photon ring test of the Kerr hypothesis: Variation in the ring shape
• Image features of spinning regular black holes based on a locality principle
• Influence of an anisotropic matter field on the shadow of a rotating black hole
• Holography of the Photon Ring
• Adaptive Analytical Ray Tracing of Black Hole Photon Rings
• Gravitational time delay effects by Kerr and Kerr-Newman black holes in strong field limits
• Black Hole Polarimetry I: A Signature of Electromagnetic Energy Extraction
• Polarimetric signatures of hot spots in black hole accretion flows
• Photon Ring Astrometry for Superradiant Clouds
• Black Hole Photon Rings Beyond General Relativity
• Testing Gravity with Black Hole Shadow Subrings
• The Black Hole Explorer: Photon Ring Science, Detection and Shape Measurement
• Maximum Observable Blueshift from Circular Equatorial Kerr Orbiters
• Study of null and time-like geodesics in the exterior of a Schwarzschild black hole with quintessence and cloud of strings
• Multi-level images around Kerr-Newman black holes
• Boundary to bound dictionary for generic Kerr orbits
• Analytical study of light ray trajectories in Kerr spacetime in the presence of an inhomogeneous anisotropic plasma
• Kerr Geodesics in Terms of Weierstrass Elliptic Functions
• Null and time-like geodesics in Kerr-Newman black hole exterior
• Polarimetric signatures of the photon ring of a black hole that is pierced by a cosmic axion string
• Bayesian Accretion Modeling: Axisymmetric Equatorial Emission in the Kerr Spacetime
• Image of the Kerr-Newman black hole surrounded by a thin accretion disk
• Birefringence Tomography for Axion Cloud
• Light echos and coherent autocorrelations in a black hole spacetime
• A Lensing-Band Approach to Spacetime Constraints
• Photon Emission from Circular Equatorial Kerr Orbiters
• Near-horizon geodesics of high-spin black holes
• Dynamics of spinning particles in Reissner-Nordström black hole exterior
• Relativistic propagation and frame dragging time delay in the timing of a pulsar orbiting the supermassive black hole SgrA*
• A Study of Black Holes in $F(R)-$ModMax Gravity: Gravitational Lensing and Constraints from EHT Observations
• Homoclinic orbits in Kerr-Newman black holes
• Bayesian Black Hole Photogrammetry
• Throat effects on strong gravitational lensing in Kerr-like wormholes
• Gravitational Lensing of Massive Particles in the Charged NUT Spacetime
• Black hole photon ring beyond General Relativity: an integrable parametrization
• Illuminating Black Hole Shadow with Dark Matter Annihilation
• Forward Ray Tracing and Hot Spots in Kerr Spacetime
• Null geodesics in extremal Kerr-Newman black holes
• Gravity versus astrophysics in black hole images and photon rings: Equatorial emissions and spherically symmetric space-times
• The appearance of a merging binary black hole very close to a spinning supermassive black hole
• High spin expansion for null geodesics
• Gravitational Lensing in the Charged NUT-de Sitter Spacetime
• Thin Accretion Disk Around Rotating Hairy Black Hole: Radiative Property and Optical Appearance
• Microlensing and event rate of static spherically symmetric wormhole
• Image of Quantum Improved Regular Kerr Black Hole and Parameter Constraints from EHT Observations
• Overlapping of photon rings in black hole imaging
• Aberration effect on lower-order images of thin accretion disk in the astrometric approach
• Optical Polarization Holonomy in the Kerr Metric
• Optical images of the Kerr-Sen black hole and thin accretion disk
• Not all spacetime coordinates for general-relativistic ray tracing are created equal
• Separability, plane wave limits and black holes
• Shadow of axisymmetric, stationary and asymptotically flat black holes in the presence of plasma
• Light propagation around a Kerr-like black hole immersed in an inhomogeneous anisotropic plasma in Rastall gravity: Analytical solutions to the equations of motion
• Phase diagrams of quasinormal frequencies for Schwarzschild, Kerr, and Taub-NUT black holes
• Gravitational Lensing in the Kerr Spacetime: An Analytic Approach for Light and High-Frequency Gravitational Waves
• Spherical particle orbits around a rotating black hole in massive gravity
• Penrose's singularity theorem and the Kerr space-time
• Massive particle surfaces and black hole shadows from intrinsic curvature
• Assessing the Role of Intrinsic Variability in Black Hole Parameter Inference using Multi-Epoch EHT Data
• Revisiting Einstein's analogy: black holes as gradient-index lenses
• Coupling constant metamorphosis, Fermat principle and light propagation in Kerr metric
• Classification of radial Kerr geodesic motion
• Gravitational Lensing by Charged Accelerating Black Holes
• An Analytical Formula for Gravitational Faraday Rotation in the ADM Split of Spacetime
• Looking through the Kerr disk
• Revisiting critical orbits of test particles traveling in a black hole background
• Arnold diffusion and geodesic dynamics of blackholes
• KAM and geodesic dynamics of blackholes
• Photon Ring Symmetries in Simulated Linear Polarization Images of Messier 87*
• Observational distinguishability of the Kerr and Kerr-Hayward metrics to EHT
• How narrow is the M87* ring? I. The choice of closure likelihood function
• Kerr isolated horizon revisited: Caustic-free congruence and adapted tetrad
• Trajectories of light beams in a Kerr metric: the influence of the rotation of an observer on the shadow of a black hole
• Observational Signatures of Kerr Black Hole Lensing