Radii of spherical photon orbits around Kerr-Newman black holes

Abstract

The spherical photon orbits around a black hole with constant radii are particular important in astrophysical observations of the black hole. In this paper, the equatorial and non-equatorial spherical photon orbits around Kerr-Newman black holes are studied. The radii of these orbits satisfy a sextic polynomial equation with three parameters, the rotation parameter $u$, charge parameter $w$ and effective inclination angle $v$. It is found that there are two polar orbits and one is inside and the other is outside the event horizon. For orbits in the equatorial plane around an extremal Kerr-Newman black hole , we find three positive solutions to the equation and provide analytical formulas for the radii of the three orbits. It is also found that a critical value of rotation parameter $u=\frac{1}{4}$ exists, above which only one retrograde orbit exists outside the event horizon and below which two orbits (one prograde and one retrograde) exist outside the event horizon. For orbits in the equatorial plane of a nonextremal Kerr-Newman black hole, there are four or two positive solutions. A critical curve in $(u,w)$-plane which separates the regions is also found. On this critical curve, the explicit formulas of three solutions are found. There always exist two equatorial photon orbits outside the event horizon in this case. For orbits between the above two special planes, there are four or two solutions to the general sextic equation. When the black hole is extremal, it is found that there is a critical inclination angle $v_{cr}$, below which only one orbit exists and above which two orbits exist outside the event horizon for a rapidly rotating black hole $u>\frac{1}{4}$. At this critical inclination angle, exact formula for the radii is also derived. Finally, a critical surface in parameter space of ($u,w,v$) is shown that separates regions with four or two solutions.

references added

References in corpus (19)

• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way
• GW190814: Gravitational Waves from the Coalescence of a 23 M${}_{\odot }$ Black Hole with a 2.6 M${}_{\odot }$ Compact Object
• First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole
• First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring
• GW190521: A Binary Black Hole Merger with a Total Mass of $150M_{\odot }$
• Black Hole Shadows, Photon Rings, and Lensing Rings
• Properties and astrophysical implications of the 150 Msun binary black hole merger GW190521
• Quasinormal-mode spectrum of Kerr black holes and its geometric interpretation
• Fundamental photon orbits: black hole shadows and spacetime instabilities
• Topological Charge and Black Hole Photon Spheres
• Upper bound on the radii of black-hole photonspheres
• Universal Properties of Light Rings for Stationary Axisymmetric Spacetimes
• Light rings of stationary spacetimes
• Strong gravitational lensing by Kerr and Kerr-Newman black holes
• On the Size of a Black Hole: The Schwarzschild is the Biggest
• Null and time-like geodesics in Kerr-Newman black hole exterior
• Exact Formulas for Spherical Photon Orbits Around Kerr Black Holes
• Lower bound on the radii of black-hole photonspheres

Cited by in corpus (3)

• Non-Equatorial Deflection of Light due to Kerr-Newman Black Hole: A Material Medium Approach
• Shadow analysis of an approximate rotating black hole solution with weakly coupled global monopole charge
• Light propagation around a Kerr-like black hole immersed in an inhomogeneous anisotropic plasma in Rastall gravity: Analytical solutions to the equations of motion