Dyonic Taub-NUT-AdS Black Branes: Thermodynamics and Phase Diagrams

TL;DR

This paper analyzes the thermodynamics of dyonic Taub-NUT-AdS black branes with flat horizons in a fixed cosmological constant setup. By relaxing the Misner-string constraints, the nut parameter $n$ is treated as a conserved charge and the first law is extended to include a conjugate potential $\phi_n$, with a two-parameter family of charges $\widetilde{Q}_e(α)$ and $\widetilde{Q}_m(α)$ that satisfy the Gibbs–Duhem relation; the total energy is $\mathfrak{M}=m-n\phi_n$. The phase structure is rich: phase diagrams in the $n$–$T$ plane reveal first-order transitions between big and small black branes and up to four critical points depending on $α$ and $\widetilde{Q}_m$, including Hawking-Page–like regions. These results illuminate the thermodynamics of Taub-NUT-AdS spacetimes with flat horizons and have potential implications for holographic duals with boundary vorticity; extensions to rotating and more general spacetimes such as Kerr-Newman-NUT in AdS or Plebanski-Demianski geometries are suggested for future work.

Abstract

Motivated by the recent developments in the thermodynamics of Taub-NUT spaces and the absence of Misner strings in Taub-NUT solutions with flat horizons, we investigated the phase structure of dyonic Taub-NUT solutions. We follow the treatment proposed in arXiv:2206.09124 and arXiv:2304.06705 to introduce the nut parameter as a conserved charge to the first law. Although the calculated quantities satisfy the first law, we have found a larger class of charges that satisfy the first law and depend on some arbitrary parameter which we call $α$. We choose to describe phase diagrams as NUT parameter-Temperature graphs to show borders of big and small black hole phases. We study the phase structure of these spaces in a mixed ensemble (i.e., we fix the electric potential, the nut parameter, and the magnetic charge), which we classify into different cases depending on the value of $α$. In some of these cases we have first-order phase transitions that end with critical points. These classes could include up to four critical points, again, depending on $α$ and the other quantities.

Figures (22)

• Figure 2.1: The boundary of spacetime at spatial infinity. the boundary consists of the top cape of $r=\infty$ and the side of the cone at $x = A$ from $r = r_h$ to $r = \infty$. The dashed line represents the hypersurface of $r = r_h$.
• Figure 2.2: The temperature of the dyonic black brane as a function of its horizon radius for $Q_m = 5$ and $\phi_e = 3$. The graph shows that for any temperature, there exists only one possible black brane solution.
• Figure 2.3: The grand potential densities of the possible phases as functions of their horizon temperature for $Q_m = 5$ and $\phi_e = 3$, the solid line represents the dyonic black brane, while the dotted line represents the extremal dyonic black brane. The graph shows that for any temperature the black brane solution always has a lower grand potential than the extremal black brane.
• Figure 3.1: The black brane horizon temperature as a function of the horizon radius in case I.I for different values of $n$. The values used to draw this graph are ($l = 1$, $\phi_e = 15$, $\alpha = 0$, $\widetilde{Q}_m = 0$). The graph shows that for $n \leq \frac{\sqrt{3}}{3}l\phi_e$ the is only one possible black brane at any temperature, while for $n > \frac{\sqrt{3}}{3}l\phi_e$ there are two possible black brane phases for $T_h \geq T_{min}$ and no possible black brane phase for $T_h < T_{min}.$
• Figure 3.2: The grand potential density of the black brane as a function of the horizon temperature in case I.I for different values of $n$. The values used to draw this graph are ($l = 1$, $\phi_e = 15$, $\alpha = 0$, $\widetilde{Q}_m = 0$). The graphs show that for $n \leq \frac{\sqrt{3}}{3}l\phi_e$ the grand potential of the black brane is always lower than that of the extremal black brane, while for $n > \frac{\sqrt{3}}{3}l\phi_e$ there is no extremal black brane, and the stable black brane always have a lower grand potential than the unstable black brane.