Thermodynamic topology of AdS black holes with FαβFγλRαγRβλ coupling in the grand canonical ensemble
Abstract
We investigate the thermodynamic and topological phase structure of charged AdS black holes with a nonminimal gauge--curvature coupling in the grand canonical ensemble. In the minimal-coupling limit ε=0, the system exhibits only Hawking--Page-like behavior and does not possess van der Waals criticality. Working perturbatively in the nonminimal coupling, we find that the ε≠0 interaction generates a rich phase structure as the electric potential is varied, including several distinct regimes of critical behavior, a double-critical region, and a regime where conventional criticality disappears. We complement the conventional thermodynamic analysis with a topological description based on the winding number of the thermodynamic vector field. The resulting rh--τ diagrams reveal that the ordering and morphology of the black-hole branches depend sensitively on both the pressure and the off-shell inverse temperature, with monotonic, disconnected, S-shaped, and cusp-like structures appearing in different parameter ranges. Remarkably, these substantial rearrangements of the solution branches can occur without changing the global winding number. In particular, the system remains in the W=+1 topological class beyond the range of conventional criticality, before eventually entering a W=0 sector. Our results demonstrate that thermodynamic topology provides complementary global information that is not captured by conventional local criticality criteria alone.
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BibTeX
@misc{rahmani2026thermodynamic,
title = {{Thermodynamic topology of AdS black holes with $F^αβF^γλR_αγR_βλ$ coupling in the grand canonical ensemble}},
author = {Faramarz Rahmani and Mehdi Sadeghi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13104},
eprint = {2609.13104},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13104},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Thermodynamic topology of AdS black holes with F^αβF^γλR_αγR_βλ coupling in the grand canonical ensemble
AU - Faramarz Rahmani
AU - Mehdi Sadeghi
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.13104
UR - https://arxiv.org/abs/2609.13104
AB - We investigate the thermodynamic and topological phase structure of charged AdS black holes with a nonminimal gauge--curvature coupling in the grand canonical ensemble. In the minimal-coupling limit ε=0, the system exhibits only Hawking--Page-like behavior and does not possess van der Waals criticality. Working perturbatively in the nonminimal coupling, we find that the ε≠0 interaction generates a rich phase structure as the electric potential is varied, including several distinct regimes of critical behavior, a double-critical region, and a regime where conventional criticality disappears. We complement the conventional thermodynamic analysis with a topological description based on the winding number of the thermodynamic vector field. The resulting r_h--τ diagrams reveal that the ordering and morphology of the black-hole branches depend sensitively on both the pressure and the off-shell inverse temperature, with monotonic, disconnected, S-shaped, and cusp-like structures appearing in different parameter ranges. Remarkably, these substantial rearrangements of the solution branches can occur without changing the global winding number. In particular, the system remains in the W=+1 topological class beyond the range of conventional criticality, before eventually entering a W=0 sector. Our results demonstrate that thermodynamic topology provides complementary global information that is not captured by conventional local criticality criteria alone.
ER -