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

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.