We investigate the extended thermodynamic properties of higher-dimensional Taub–NUT/Bolt–AdS spaces where a cosmological constant is treated as a pressure. We find a general form for thermodynamic volumes of Taub–NUT/Bolt–AdS black holes for arbitrary dimensions. Interestingly, it is found that the Taub–NUT–AdS metric has a thermodynamically stable range when the total number of dimensions is a multiple of 4 (4, 8, 12, …). We also explore their phase structure and find the first order phase transition holds for higher-dimensional cases.
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Chong Oh Lee (2014) studied this question.
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