Revisiting critical orbits of test particles traveling in a black hole background
arXiv:2602.09568 · doi:10.1088/1674-1137/ae5d29
Abstract
This paper systematically revisits the critical orbits of test particles in various black hole backgrounds, including Schwarzschild, Reissner-Nordström, Kerr, and Kerr-Newman spacetimes. We identify the critical orbits directly from the root structure of the radial equation, and we provide explicit expressions that relate the relevant parameters - energy, angular momentum, and charge-to-mass ratio - to the critical radius, as well as explicit formulas for the critical orbits in each case. Special attention is given to the relationships among the photon spheres, black hole shadows, and critical null geodesics. We also present extensive numerical results.
References in corpus (29)
- Perturbative Approach to an orbital evolution around a Supermassive black hole
- Lensing by Kerr Black Holes
- Analytical solutions of bound timelike geodesic orbits in Kerr spacetime
- Analytical solution of the geodesic equation in Kerr-(anti) de Sitter space-times
- Geodesic equation in Schwarzschild--(anti-)de Sitter space--times: Analytical solutions and applications
- The Null Geodesics of the Kerr Exterior
- Complete analytic solution of the geodesic equation in Schwarzschild--(anti) de Sitter space--times
- Geodesics of electrically and magnetically charged test particles in the Reissner-Nordström space-time: analytical solutions
- Analytic solutions of the geodesic equation in higher dimensional static spherically symmetric space-times
- Analytic treatment of complete and incomplete geodesics in Taub-NUT space-times
- Equatorial circular orbits of neutral test particles in the Kerr--Newman spacetime
- Homoclinic Orbits around Spinning Black Holes I: Exact Solution for the Kerr Separatrix
- Charged particle motion in Kerr-Newmann space-times
- Off-equatorial orbits in strong gravitational fields near compact objects
- Accretion of a relativistic, collisionless kinetic gas into a Schwarzschild black hole
- Homoclinic Orbits around Spinning Black Holes II: The Phase Space Portrait
- Accretion of Dark Matter onto a Moving Schwarzschild Black Hole: An Exact Solution
- Completing characterization of photon orbits in Kerr and Kerr-Newman metrics
- Geodesic Motion of Neutral Particles around a Kerr-Newman Black Hole
- Accretion of the relativistic Vlasov gas onto a moving Schwarzschild black hole: Exact solutions
- Spherical steady-state accretion of a relativistic collisionless gas into a Schwarzschild black hole
- Null and time-like geodesics in Kerr-Newman black hole exterior
- Kerr Geodesics in Terms of Weierstrass Elliptic Functions
- Accretion of the Vlasov gas on Reissner-Nordström black holes
- Revisiting timelike and null geodesics in the Schwarzschild spacetime: general expressions in terms of Weierstrass elliptic functions
- Schwarzschild geodesics in terms of elliptic functions and the related red shift
- Null geodesics in extremal Kerr-Newman black holes
- Timelike and null geodesics in the Schwarzschild space-time: Analytical solutions
- Accretion of the degenerate Fermi gas onto a Reissner-Nordström black hole