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arXiv · 2512.04478

Thermodynamic geometric analysis of D-dimensional RN black hole

Wen-Xiang Chen
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Abstract

This paper studies the thermodynamics and Ruppeiner geometry of D-dimensional RN black holes. We analyze the thermodynamic curvature scalar $R$ in various thermodynamic ensembles. It is found that in an ensemble of fixed charge (canonical ensemble), the Ruppeiner curvature is curved and diverges at a critical point, indicating the existence of a phase transition for $D > 4$. In contrast, when all extensive variables are allowed to fluctuate (for example, in a grand-canonical ensemble or with pressure fixed), the Ruppeiner geometry can appear flat. We also demonstrate that the thermodynamic geometric metric has a one-to-one correspondence with the periodicity of the Euclidean path integral method. In particular, the inverse temperature (the Euclidean time period) serves as a bridge connecting the thermodynamic geometry and the Euclidean action approach.

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Wen-Xiang Chen. 2025-12-04. Thermodynamic geometric analysis of D-dimensional RN black hole. https://arxiv.org/abs/2512.04478

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