Dyonic Taub–NUT–AdS black branes: thermodynamics and phase diagrams

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 study the phase structure of the dyonic Taub–NUT solutions with Lorentzian signature. 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 $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> . We choose to describe phase diagrams as NUT parameter-temperature graphs to show borders of big and small black brane phases. We study the phase structure of these spaces in a mixed ensemble (i.e., fixed electric potential, NUT charge, and magnetic charge), which we classify into different cases depending on the value of $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> and the other quantities. Most of these cases not only have first-order phase transitions, but also, end at critical points. Some of these cases include up to four critical points, depending on the value of $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> and the other quantities.