Abstract
We examine the thermodynamics of Euclidean dyonic Taub-Nut/Bolt-AdS4 black holes for a variety of horizon geometries to understand how gauge field regularity conditions influence the thermodynamic relations. We find several distinct features that distinguish the NUT-charged case from its dyonic Reissner-Nordstrom counterpart. For the Nut solution, the gauge field vanishes at the horizon and so regularity is ensured. For the Bolt solution we find that the norm of the gauge field is required to vanish at the horizon in order to satisfy both regularity and the first law of thermodynamics. This regularity condition yields a constraint on the electric and magnetic charges and so reduces cohomogeneity of the system; for spherical horizons, the regularity condition removing the Misner string singularity further reduces cohomogeneity. We observe that bolt solutions with increasing electric charge have positive heat capacity, but upon turning on the magnetic charge to make the solution dyonic, we find that the properties of the uncharged one are retained, having both positive and negative heat capacity. We also study the extremal Bolt solution, finding that Misner string disappears at the horizon in the zero temperature limit. We find that the extremal solution has finite-temperature-like behaviour, with the electric potential playing a role similar to temperature.
Highlights
These spacetimes have peculiar properties when their horizon geometry is a sphere due to the non-trivial fibration of time on S2, which induces a spurious singularity in a given coordinate system
We examine the thermodynamics of Euclidean dyonic Taub-Nut/Bolt-AdS4 black holes for a variety of horizon geometries to understand how gauge field regularity conditions influence the thermodynamic relations
We observe that bolt solutions with increasing electric charge have positive heat capacity, but upon turning on the magnetic charge to make the solution dyonic, we find that the properties of the uncharged one are retained, having both positive and negative heat capacity
Summary
This automatically agrees with the condition for removal of the Misner string.When κ = −1, fn becomes negative near the horizon limit r = χ +. This happens because r = χ is not the outermost horizon, but instead is contained in a bolt solution whose horizon is 4χ2 − κl2 − χ [27]. The thermodynamic entropy and energy are obtained from These quantities satisfy the first law and free energy dE = TndS, F = E − TnS (2.20). Since the Misner string is not present, we expect that the entropy satisfies the Bekenstein-Hawking entropy and so becomes the area of the TN-AdS, which is zero
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