Thermodynamic Volumes of Extended Black Hole Thermodynamics with Auxiliary Gauge Fields
Abstract
By applying the Iyer-Wald formalism to the modified Lagrangian form for the gravitational system, where the coupling constants appearing in the original Lagrangian form, such as the cosmological constant, are promoted to the dynamical scalar fields by introducing the corresponding auxiliary gauge fields, we derive the first law of the extended black hole thermodynamics, where the resulting thermodynamic volumes as the conjugate thermodynamic variables to the coupling constants are nevertheless independent of the auxiliary gauge fields and exactly the same as those obtained before via varying the coupling constants by brute force. In addition, it is further shown that such volumes can also be expressed in terms of the auxiliary gauge fields and evaluated on the black hole horizon, validating the proposal made in the previous literature.
Versions
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BibTeX
@misc{mou2026thermodynamic,
title = {{Thermodynamic Volumes of Extended Black Hole Thermodynamics with Auxiliary Gauge Fields}},
author = {Zili Mou and Yu Tian and Hongbao Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05022},
eprint = {2610.05022},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05022},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Thermodynamic Volumes of Extended Black Hole Thermodynamics with Auxiliary Gauge Fields
AU - Zili Mou
AU - Yu Tian
AU - Hongbao Zhang
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.05022
UR - https://arxiv.org/abs/2610.05022
AB - By applying the Iyer-Wald formalism to the modified Lagrangian form for the gravitational system, where the coupling constants appearing in the original Lagrangian form, such as the cosmological constant, are promoted to the dynamical scalar fields by introducing the corresponding auxiliary gauge fields, we derive the first law of the extended black hole thermodynamics, where the resulting thermodynamic volumes as the conjugate thermodynamic variables to the coupling constants are nevertheless independent of the auxiliary gauge fields and exactly the same as those obtained before via varying the coupling constants by brute force. In addition, it is further shown that such volumes can also be expressed in terms of the auxiliary gauge fields and evaluated on the black hole horizon, validating the proposal made in the previous literature.
ER -