Offshell thermodynamic metrics of the Schwarzschild black hole

Abstract

Thermodynamic metric usually works only for those black holes with more than one conserved charge, therefore the Schwarzschild black hole was excluded. In this letter, we compute and compare different versions of offshell thermodynamic metric for the Schwarzschild-like black hole by introducing a new degree of freedom. This new degree of freedom could be the running Newton constant, a cutoff scale for regular black hole, a noncommutative deformation, or the deformed parameter in the nonextensive Tsallis-Renyi entropy. The onshell metric of the deformed Schwarzschild solution would correspond to the submanifold by gauge fixing of this additional degree of freedom. In particular, the thermal Ricci scalar for the Schwarzschild black hole, though different for various deformation, could be obtained by switching off the deformation.

15 pages, 22 figures, 1 table

References in corpus (16)

• Geometrothermodynamics
• Formulation of the uncertainty relations in terms of the Renyi entropies
• Rényi entropy and the thermodynamic stability of black holes
• Einstein-Born-Infeld-Massive Gravity: adS-Black Hole Solutions and their Thermodynamical properties
• Phase transition and Thermodynamical geometry of Reissner-Nordström-AdS Black Holes in Extended Phase Space
• Phase transition and thermodynamic geometry of Einstein-Maxwell-dilaton black holes
• Charged Dilatonic Black Holes in Gravity's Rainbow
• A new approach toward geometrical concept of black hole thermodynamics
• Phase transition and thermodynamical geometry for Schwarzschild AdS black hole in $Ad{S}_5\times S^5$ spacetime
• Massive charged BTZ black holes in asymptotically (a)dS spacetimes
• New perspective for black hole thermodynamics in Gauss-Bonnet-Born-Infeld massive gravity
• Geometrical method for thermal instability of nonlinearly charged BTZ Black Holes
• Hessian matrix, specific heats, Nambu brackets, and thermodynamic geometry
• Phase transition of charged Black Holes in Brans-Dicke theory through geometrical thermodynamics
• Geometrothermodynamics of black holes in Lovelock gravity with a nonlinear electrodynamics
• Einstein-Maxwell-Dilatonic phantom black holes: Thermodynamics and geometrothermodynamics

Cited by in corpus (6)

• Tsallis Holographic Dark Energy
• Generalized entropy formalism and a new holographic dark energy model
• Area-law versus Rényi and Tsallis black hole entropies
• Effects of Anisotropy on the Sign-Changeable Interacting Tsallis Holographic Dark Energy
• Thermal fluctuations of (non)linearly charged BTZ black hole in massive gravity
• AdS to dS phase transition mediated by thermalon in Einstein-Gauss-Bonnet gravity from Renyi statistics