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Abstract In this paper, via employing the uniformly modified form of the generalized off-shell Helmholtz free energy, we investigate the topological numbers for the four-dimensional neutral Lorentzian Taub–NUT, Taub–NUT–AdS and Kerr–NUT spacetimes, and find that these solutions can also be classified into one of three types of those well-known black hole solutions, which implies that these spacetimes should be viewed as generic black holes from the viewpoint of the thermodynamic topological approach.
Di Wu (Fri,) studied this question.
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