Rényi Entropy and the Topological Features of Charged AdS Black Hole

Abstract

This study applies Duan's topological current $\varphi$-mapping theory to investigate a newly proposed charged modified AdS black hole using the Rényi entropy formalism, examining its thermodynamic properties across the canonical, mixed, and grand canonical ensembles.} Electric and magnetic charges are fixed in the canonical ensemble, whereas the mixed ensemble incorporates electric and magnetic potentials. The grand canonical ensemble, meanwhile, ensures consistency by employing these potentials exclusively. Initially, we compute topological charges by identifying critical points in each ensemble. In both the canonical and mixed ensembles, we identify a conventional critical point with a topological charge of $-1$. We then model the black hole's domain in the AdS regime as a topological defect in thermodynamic space and analyze its local and global topology by calculating the winding numbers at these defect locations. {Interestingly, the canonical and mixed ensembles exhibit identical black hole topologies, each possessing a total topological charge of $1$ within the framework of the Rényi entropy.} Finally, we characterize the canonical, mixed, and grand canonical ensembles based on the presence of generation/annihilation points: the canonical ensemble has one such point, the mixed ensemble has a negative one, and the grand canonical ensemble has none.

18 pages, 17 captioned figures, published in Chin. J. Phys

References in corpus (25)

• Light ring stability in ultra-compact objects
• A non-linear duality-invariant conformal extension of Maxwell's equations
• Black Hole Solutions as Topological Thermodynamic Defects
• Stationary black holes and light rings
• Topology of black hole thermodynamics
• Topological classes of thermodynamics of rotating AdS black holes
• 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
• Upper bound on the radii of black-hole photonspheres
• Topological interpretation for phase transitions of black holes
• The topological natures of the Gauss-Bonnet black hole in AdS space
• Accelerated Black Holes beyond Maxwell's Electrodynamics
• 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
• Bulk-boundary thermodynamic equivalence: a topology viewpoint
• Distinct topological configurations of equatorial timelike circular orbit for spherically symmetric (hairy) black holes
• Vortex/anti-vortex pair creation in black hole thermodynamics
• Topological classes of black holes in de-Sitter spacetime
• Kerr-de Sitter and Kerr-anti-de Sitter black holes as accelerators for spinning particles
• Path integral and instantons for the process and phase transition rate of the RNAdS black hole
• Topological classes of BTZ black holes
• Thermodynamics of Asymptotically de-Sitter Black Hole in dRGT Massive Gravity from Rényi entropy

Cited by in corpus (2)

• Topology of black hole thermodynamics: A brief review
• Thermodynamic and observational implications of black holes in toroidal geometry