Abstract
We investigate the thermodynamic behaviour of Lorentzian Dyonic Taub-NUT Black Hole spacetimes. We consider two possibilities in their description: one in which their entropy is interpreted to be one quarter of the horizon area (the horizon entropy), and another in which the Misner string also contributes to the entropy (the Noether charge entropy). We find that there can be as many as three extremal black holes (or as few as zero) depending on the choice of parameters, and that the dependence of the free energy on temperature — and the resultant phase behaviour — depends very much on which of these situations holds. Some of the phase behaviour we observe holds regardless of which interpretation of the entropy holds. However another class of phase transition structures occurs only if the Noether charge interpretation of the entropy is adopted.
Highlights
Pathologies [14, 15]
We investigate the thermodynamic behaviour of Lorentzian Dyonic Taub-NUT Black Hole spacetimes
All thermodynamic quantities are finite for all finite values of the NUT charge n, and have a smooth limit as the n → 0. It was subsequently argued [19] that the surface gravity of the black hole and its conjugate areal quantity should respectively correspond to the temperature and entropy of the LTN black hole, with an additional conjugate pair of variables corresponding to the surface gravity of the Misner strings and a conjugate Misner charges, the N/S corresponding to the north/south polar axes
Summary
The Noether charge entropy SN contains contributions from both the horizon and the Misner string, with NN and ψN the corresponding thermodynamic NUT charge and conjugate potential. To relate these two we can write. The Noether charge approach ascribes the total thermodynamic entropy as having contributions from both the horizon and the Misner string [5] 3. A constrained thermodynamics where the electric and magnetic charges are related by imposing the constraint that the electromagnetic potential A in (2.2) vanishes at the horizon [10, 44, 45]. In what follows we shall adopt the perspective that SN is regarded as the entropy, and will comment where relevant as to what distinctions arise if S+ is regarded as the entropy
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