https://doi.org/10.1140/epjc/s10052-026-15289-9
Regular Article - Theoretical Physics
Thermodynamic topology of Einstein–Maxwell-dilaton theories
1
Institute of Fundamental Physics and Quantum Technology, and School of Physical Science and Technology, Ningbo University, 315211, Ningbo, Zhejiang, China
2
Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran
3
Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, 14476, Golm, Germany
a
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Received:
18
November
2025
Accepted:
31
December
2025
Published online:
26
January
2026
Abstract
We present a systematic investigation of the thermodynamic topology for a broad class of asymptotically charged Anti-de Sitter (AdS) black holes in Einstein–Maxwell-Dilaton (EMD) theories, examining how scalar coupling parameters and spacetime dimensions influence black hole thermodynamics. Employing a topological approach that utilizes the torsion number of vector fields constructed from the generalized free energy, we characterize black hole states as topological defects within the thermodynamic parameter space. Through analytical solutions spanning dimensions 
and 
including the Gubser–Rocha model, we demonstrate that variations in the dilaton coupling constant 
particularly near its critical value 
induce transitions between distinct thermodynamic topological phases. Our analysis reveals that certain black hole solutions constitute a novel class designated as 
characterized by a torsion number 
that corresponds to a unique stability structure. We establish that Gubser–Rocha models belong to this topological classification. These results significantly expand the existing classification framework while reinforcing thermodynamic topology as a robust analytical tool for probing the universal properties of black holes in both gravitational and holographic contexts. The findings provide new insights into the relationship between microscopic couplings and macroscopic thermodynamic behavior in extended gravity theories.
© The Author(s) 2026
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