Distinct topological configurations of equatorial timelike circular orbit for spherically symmetric (hairy) black holes

Abstract

Topology is a promising approach toward to the light ring in a generic black hole background, and equatorial timelike circular orbit in a stationary black hole background. In this paper, we consider the distinct topological configurations of the timelike circular orbits in static, spherically symmetric, and asymptotic flat black holes. By making use of the equation of motion of the massive particles, we construct a vector with its zero points exactly relating with the timelike circular orbits. Since each zero point of the vector can be endowed with a winding number, the topology of the timelike circular orbits is well established. Stable and unstable timelike circular orbits respectively have winding number +1 and -1. In particular, for given angular momentum, the topological number of the timelike circular orbits also vanishes whether they are rotating or not. Moreover, we apply the study to the Schwarzschild, scalarized Einstein-Maxwell, and dyonic black holes, which have three distinct topological configurations, representations of the radius and angular momentum relationship, with one or two pairs timelike circular orbits at most. It is shown that although the existence of scalar hair and quasi-topological term leads to richer topological configurations of the timelike circular orbits, they have no influence on the total topological number. These results indicate that the topological approach indeed provides us a novel way to understand the timelike circular orbits. Significantly, different topological configurations can share the same topology number, and hence belong to the same topological class. More information is expected to be disclosed when other different topological configurations are present.

arXiv comment20 pages, 14 figures. Title is changed. Published version

References in corpus (34)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole
• GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence
• GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2
• 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?
• Foundations of Black Hole Accretion Disk Theory
• Spontaneous scalarization of black holes and compact stars from a Gauss-Bonnet coupling
• 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
• Photon Rings around Kerr and Kerr-like Black Holes
• Topology of black hole thermodynamics
• Spontaneous scalarisation of charged black holes: coupling dependence and dynamical features
• Topological Charge and Black Hole Photon Spheres
• Analytical representation for metrics of scalarized Einstein-Maxwell black holes and their shadows
• Photon Spheres and Spherical Accretion Image of a Hairy Black Hole
• Einstein-scalar-Gauss-Bonnet black holes: Analytical approximation for the metric and applications to calculations of shadows
• Universal Properties of Light Rings for Stationary Axisymmetric Spacetimes
• Gravitational lensing in spherically symmetric static spacetimes with centrifugal force reversal
• Shadows and lensing of black holes immersed in strong magnetic fields
• Charged black holes with axionic-type couplings: classes of solutions and dynamical scalarisation
• Light rings of stationary spacetimes
• Topology of equatorial timelike circular orbits around stationary black holes
• Evolution of the Chern-Simons Vortices
• Quasinormal Modes of Black Holes with Multiple Photon Spheres
• Area bound for a surface in a strong gravity region
• Equatorial timelike circular orbits around generic ultracompact objects
• Gravitational Lensing by Black Holes with Multiple Photon Spheres
• Dynamical photon sphere and time evolving shadow around black holes with temporal accretion
• The fate of observers in circular motion

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• ${\tilde{W}}^{1+}$ subclass: Extending the topological classification of black hole thermodynamics
• Aschenbach effect and circular orbits in static and spherically symmetric black hole backgrounds
• The Existence and Distribution of Photon Spheres Near Spherically Symmetric Black Holes -- A Geometric Analysis
• Spherically symmetric configurations in the quadratic $f(R)$ gravity
• A class of Taub-NUT-scalar metrics via Ehlers transformations
• 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
• Static spheres and Aschenbach effect for black holes in massive gravity
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• Thermodynamic topology of dyonic AdS black holes with quasitopological electromagnetism in Einstein-Gauss-Bonnet gravity
• The $D$-dimensional charged AdS black holes solutions in polytropic dark energy from Barrow entropy
• Dimensional structure of thermodynamic topology in ultraspinning Kerr-AdS black holes
• Robust topological invariants of timelike circular orbits for spinning test particles in black hole spacetimes
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