Topological classes of higher-dimensional black holes in massive gravity

Abstract

In this paper, we study topological numbers for five-, six- and seven-dimensional anti-de Sitter black holes in the ghost-free massive gravity. We find that when the black holes are charged, they have the same topological number. The topological numbers for the uncharged black holes are 0 or 1, and the specific values are determined by the values of the black holes' parameters. Since $k$ and $c_0^2{c}_2{m}^2$ appear together in the generalized free energy in the form of $k+c_0^2{c}_2{m}^2$, where $k$ characterizes the horizon curvature and $c_2{m}^2$ is the coefficient of the second term of massive potential associated with the graviton mass, this result is applicable to the black holes with the spherical, Ricci flat or hyperbolic horizons. This work shows that the parameters of the ghost-free massive gravity play an important role in topological classes of black holes.

21 pages, 13 figures

References in corpus (27)

• P-V criticality of charged AdS black holes
• Enthalpy and the Mechanics of AdS Black Holes
• Pressure and volume in the first law of black hole thermodynamics
• Light ring stability in ultra-compact objects
• Thermodynamics of Black Holes in Massive Gravity
• P-V criticality in the extended phase space of black holes in massive gravity
• Black Hole Solutions as Topological Thermodynamic Defects
• Stationary black holes and light rings
• van der Waals like behaviour of topological AdS black holes in massive gravity
• Topology of black hole thermodynamics
• Einstein-Born-Infeld-Massive Gravity: adS-Black Hole Solutions and their Thermodynamical properties
• Topological classes of thermodynamics of rotating AdS black holes
• Topological Charge and Black Hole Photon Spheres
• Topology of black hole thermodynamics in Lovelock gravity
• Topological classes of rotating black holes
• Topology of critical points and Hawking-Page transition
• Revisiting thermodynamic topologies of black holes
• Classifying topology of consistent thermodynamics of the four-dimensional neutral Lorentzian NUT-charged spacetimes
• Behavior of quasinormal modes and Van der Waals-like phase transition of charged AdS black holes in massive gravity
• Universal Properties of Light Rings for Stationary Axisymmetric Spacetimes
• Topological interpretation for phase transitions of black holes
• The topological natures of the Gauss-Bonnet black hole in AdS space
• Intrinsic curvature and topology of shadows in Kerr spacetime
• Light rings of stationary spacetimes
• Thermal Dynamic Phase Transition of Reissner-Nordström Anti-de Sitter Black Holes on Free Energy Landscape
• Topology of equatorial timelike circular orbits around stationary black holes
• Thermodynamics and weak cosmic censorship conjecture in extended phase spaces of anti-de Sitter black holes with particles' absorption

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