Topological Charge and Black Hole Photon Spheres

Abstract

Black hole photon spheres or light rings are closely linked to astronomical phenomena, such as the gravitational waves and the shadow in spherically symmetric or axi-symmetric spacetime. In Cunha and Herdeiro [Phys. Rev. Lett. 124, 181101 (2020)], a topological argument was applied for the four dimensional stationary, axi-symmetric, asymptotically flat black hole, and the result indicates that at least, there exists one standard light ring outside the black hole horizon for each rotation sense. Inspired by it, in this paper, we would like to consider a similar issue for a nonrotating, static, spherically symmetric black hole not only with asymptotically flat behavior, but also with AdS and dS behaviors. Following Duan's topological current $\varphi$-mapping theory, the topological current and charge for the photon spheres are introduced. The topological current is nonzero only at the zero point of the vector field determining the location of the photon sphere. So each photon sphere can be assigned a topological charge. Considering the full exterior region, we find the total topological charge always equals -1. This result confirms that there exists at least one standard photon sphere outside of the black hole not only in asymptotically flat spacetime, but also in asymptotically AdS and dS spacetime. Then we apply the study to the dyonic black holes. We observe that even when more photon spheres are included, the total topological charge stays unchanged. Moreover, for a naked singularity, it has a vanishing topological charge, indicating that the black hole and naked singularity are in different topological classes. It is expected that this novel topological argument could provide an insightful idea on the study of the black hole photon spheres or light rings, and further cast new light on the black hole astronomical phenomena.

arXiv comment12 pages, 8 figures, and 2 tables. Dedicated to the memory of Prof. Yi-Shi Duan

References in corpus (19)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• 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
• Geodesic stability, Lyapunov exponents and quasinormal modes
• Is the gravitational-wave ringdown a probe of the event horizon?
• The geometry of photon surfaces
• Shadows and strong gravitational lensing: a brief review
• Light ring stability in ultra-compact objects
• Stationary black holes and light rings
• Connection between black-hole quasinormal modes and lensing in the strong deflection limit
• Quasinormal modes of Kerr-Newman black holes: coupling of electromagnetic and gravitational perturbations
• Upper bound on the radii of black-hole photonspheres
• Post-Kerr black hole spectroscopy
• Intrinsic curvature and topology of shadows in Kerr spacetime
• Evolution of the Chern-Simons Vortices
• Relationship between High-Energy Absorption Cross Section and Strong Gravitational Lensing for Black Hole
• Regge poles of the Schwarzschild black hole: a WKB approach
• Establishing a universal relation between gravitational waves and black hole lensing

Cited by in corpus (65)

• Black Hole Solutions as Topological Thermodynamic Defects
• Topology of black hole thermodynamics
• Topological classes of thermodynamics of rotating AdS black holes
• Topology of black hole thermodynamics in Gauss-Bonnet gravity
• Topological classes of rotating black holes
• Consistent thermodynamics and topological classes for the four-dimensional Lorentzian charged Taub-NUT spacetimes
• Topology of critical points and Hawking-Page transition
• Classifying topology of consistent thermodynamics of the four-dimensional neutral Lorentzian NUT-charged spacetimes
• Light rings and shadows of static black holes in effective quantum gravity
• Universal Properties of Light Rings for Stationary Axisymmetric Spacetimes
• Topological interpretation for phase transitions of black holes
• Topological classes of thermodynamics of the four-dimensional static accelerating black holes
• Shadows and lensing of black holes immersed in strong magnetic fields
• Thermodynamic Topology and Photon Spheres in the Hyperscaling violating black holes
• Light rings of stationary spacetimes
• Topology of equatorial timelike circular orbits around stationary black holes
• Topological classes of thermodynamics of the static multi-charge AdS black holes in gauged supergravities: novel temperature-dependent thermodynamic topological phase transition
• The Role of Topological Photon Spheres in Constraining the Parameters of Black Holes
• Distinct topological configurations of equatorial timelike circular orbit for spherically symmetric (hairy) black holes
• Universal thermodynamic topological classes of rotating black holes
• Topological classes of thermodynamics of the rotating charged AdS black holes in gauged supergravities
• Black Holes with Multiple Photon Spheres
• Thermodynamic Topology of $D=4,5$ Horava Lifshitz Black Hole in Two Ensembles
• Static spheres around spherically symmetric black hole spacetime
• Topological interpretation of extremal and Davies-type phase transitions of black holes
• Bulk-boundary and RPS Thermodynamics from Topology perspective
• Topological classes of higher-dimensional black holes in massive gravity
• On Thermal Stability of Hairy Black Holes
• Mutual Influence of Photon Sphere and Non-Commutative Parameter in Various Non-Commutative Black Holes: Part I- Towards evidence for WGC
• Effective Potential and Topological Photon Spheres: A Novel Approach to Black Hole Parameter Classification
• Black Hole Chemistry: the first 15 years
• Rényi Topology of Charged-flat Black Hole: Hawking-Page and Van-der-Waals Phase Transitions
• Light rings and shadows of static black holes in effective quantum gravity II: A new solution without Cauchy horizons
• WGC as WCCC protector: The Synergistic Effects of various Parameters in Identifying WGC candidate Models
• Mechanisms Behind the Aschenbach Effect in Non-Rotating Black Hole Spacetime
• Topology of Born-Infeld-AdS Black Hole Phase Transitions: Bulk and CFT Sides
• Thermodynamic topological classes of the rotating, accelerating black holes
• Thermodynamic Topology of Kiselev-AdS Black Holes within f (R, T) gravity
• Triple points and novel phase transitions of dyonic AdS black holes with quasitopological electromagnetism
• Twisting shadows: Light rings, lensing and shadows of black holes in swirling universes
• Thermodynamic analysis of black holes with cloud of strings and quintessence via Barrow entropy
• Universal thermodynamic topological classes of three-dimensional BTZ black holes
• Topology of black hole phase transition in JT gravity
• Thermodynamic Curvature and Topological Insights of Hayward Black Holes with String Fluids
• Aschenbach effect and circular orbits in static and spherically symmetric black hole backgrounds
• Gravitational signatures of a nonlinear electrodynamics in $f(R,T)$ gravity
• ${\tilde{W}}^{1+}$ subclass: Extending the topological classification of black hole thermodynamics
• Radii of spherical photon orbits around Kerr-Newman black holes
• Topology of the charged AdS black hole in restricted phase space
• Multimodal signatures of asymptotic (A)dS Kalb-Ramond black holes: Constraints through the shadow, weak deflection angle, and topological photon spheres
• A class of Taub-NUT-scalar metrics via Ehlers transformations
• Remarks on the light ring images and the optical appearance of hairy black holes in Einstein-Maxwell-dilaton gravity
• Thermodynamics and topological classifications of static non-extremal four-charge AdS black hole in the five-dimensional $\mathcal{N}=2$, $STU-W^{2}U$ gauged supergravity
• Infrared Extended Uncertainty Principle Corrections and Quintessence-Induced Topology of Reissner-Nordström AdS Black Holes
• Assessing WGC Compatibility in ModMax Black Holes via Photon Spheres Analysis and WCCC Validation
• Light rings in static and extremal black holes
• Thermodynamic Topology and Photon Spheres Analysis of Black Holes in Brane-World: Insights from Barrow Entropy
• Topology of black hole thermodynamics: A brief review
• The $D$-dimensional charged AdS black holes solutions in polytropic dark energy from Barrow entropy
• Optical, Dynamic and Topological Characteristics of Deformed Schwarzschild Black Holes
• Gravitational aspects of a new bumblebee black hole
• Robust topological invariants of timelike circular orbits for spinning test particles in black hole spacetimes
• Dimensional structure of thermodynamic topology in ultraspinning Kerr-AdS black holes
• Imprints of Topological Thermodynamics on Black Hole Dynamics
• Topological charge and black hole photon spheres in massive gravity