Thermodynamics of Taub-NUT and Plebanski Solutions

Abstract

We observe the parallel between the null Killing vector on the horizon and degenerate Killing vectors at both north and south poles in Kerr-Taub-NUT and general Plebanski solutions. This suggests a correspondence between the pairs of the angular momentum/velocity and the NUT charge/potential. We treat the time as a real line such that the Misner strings are physical. We find that the NUT charge spreads along the Misner strings, analogous to that the mass in the Schwarzschild black hole sits at its spacetime singularity. We develop procedures to calculate all the thermodynamic quantities and we find that the results are consistent with the first law (Wald formalism), the Euclidean action and the Smarr relation. We also apply the Wald formalism, the Euclidean action approach, and the (generalized) Komar integration to the electric and magnetic black holes in a class of EMD theories, and also to boosted black strings and Kaluza-Klein monopoles in five dimensions, to gain better understandings of how to deal with the subtleties associated with Dirac and Misner strings.

Latex, 43 pages, 4 graphs grouped into 1 figure, typos corrected, references added and comments revised and added, more typos corrected

References in corpus (9)

• Holographic Complexity Equals Which Action?
• General Smarr relation and first law of Nutty dyonic black hole
• Consistent mass formulas for the four-dimensional dyonic NUT-charged spacetimes
• Lorentzian Taub-NUT spacetimes: Misner string charges and the first law
• The First Law for the Lorentzian Rotating Taub-NUT
• Dual Charges for AdS Spacetimes and the First Law of Black Hole Mechanics
• Thermodynamics of Dyonic NUT Charged Black Holes with Entropy as Noether Charge
• Topological dyonic Taub-Bolt/NUT-AdS: Thermodynamics and first law
• Improved Wald formalism and First Law of Dyonic Black Strings with Mixed Chern-Simons Terms

Cited by in corpus (15)

• Consistent thermodynamics and topological classes for the four-dimensional Lorentzian charged Taub-NUT spacetimes
• Classifying topology of consistent thermodynamics of the four-dimensional neutral Lorentzian NUT-charged spacetimes
• Black Hole Chemistry: the first 15 years
• Thermodynamics of accelerating AdS${}_4$ black holes from the covariant phase space
• Fermionic and Bosonic Greybody Factors as well as Quasinormal Modes for Charged Taub NUT Black Holes
• Consistent mass formulas for higher even-dimensional Taub-NUT spacetimes and their AdS counterparts
• First law of black hole thermodynamics and the weak cosmic censorship conjecture for Kerr-Newman Taub-NUT black holes
• Consistent mass formulas for higher even-dimensional Reissner-Nordström-NUT-AdS spacetimes
• Leading Higher Derivative Corrections to Multipole Moments of Kerr-Newman Black Hole
• Conical singularity in spacetimes with NUT is observer-dependent
• Thermodynamic law and holography dual of accelerating and rotating black hole in Nariai limit
• Charged Taub-NUT-de Sitter spacetime in DGP braneworld and its thermodynamics
• Test fields and naked singularities: is the second law the cosmic censor?
• Metallic transports from Taub-NUT AdS black holes
• New Lorentzian Taub-NUT and Euclidean Eguchi-Hanson Solutions in $f(R)$ gravity