Jordan-like invariant representations of scalar-tensor gravity and the return of imperfect-fluid thermodynamics
Abstract
It has been shown that the thermodynamics of frame-invariant scalar-tensor gravity admits an Einstein-frame-like invariant representation, in which the scalar sector is minimally coupled and behaves as a perfect fluid with vanishing temperature. We show that this is not the only invariant thermodynamic organization available. Using instead the invariant matter metric, we construct a Jordan-frame-like invariant representation in which matter is minimally coupled and the gravitational action takes the Brans-Dicke-Bergmann-Wagoner form with invariant fields Ψ=ℐ1−1, 𝒰(Ψ), and ωinv(Ψ). In this representation the metric field equations retain the Hessian sector characteristic of Jordan-frame scalar-tensor gravity. A 1+3 decomposition of the corresponding effective stress tensor yields nonvanishing heat flux and anisotropic stress in a generic congruence. In the Ψ-comoving frame, the usual first-order thermodynamic identifications are recovered in invariant form, including KJTJ=−Ψ̇/(κ2Ψ) and ηJ=Ψ̇/(2κ2Ψ), with the bulk channel obtained in homogeneous and isotropic sectors. Thus, frame-invariant scalar-tensor thermodynamics is not intrinsically restricted to an Einstein-frame-like perfect-fluid description: it also admits a Jordan-frame-like invariant formulation in which the effective imperfect-fluid interpretation is manifest.
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BibTeX
@misc{pereira2026jordanlike,
title = {{Jordan-like invariant representations of scalar-tensor gravity and the return of imperfect-fluid thermodynamics}},
author = {David S. Pereira and José Pedro Mimoso},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20189},
eprint = {2609.20189},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20189},
}
RIS
TY - UNPB
TI - Jordan-like invariant representations of scalar-tensor gravity and the return of imperfect-fluid thermodynamics
AU - David S. Pereira
AU - José Pedro Mimoso
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.20189
UR - https://arxiv.org/abs/2609.20189
AB - It has been shown that the thermodynamics of frame-invariant scalar-tensor gravity admits an Einstein-frame-like invariant representation, in which the scalar sector is minimally coupled and behaves as a perfect fluid with vanishing temperature. We show that this is not the only invariant thermodynamic organization available. Using instead the invariant matter metric, we construct a Jordan-frame-like invariant representation in which matter is minimally coupled and the gravitational action takes the Brans-Dicke-Bergmann-Wagoner form with invariant fields Ψ=ℐ_1^−1, 𝒰(Ψ), and ω_inv(Ψ). In this representation the metric field equations retain the Hessian sector characteristic of Jordan-frame scalar-tensor gravity. A 1+3 decomposition of the corresponding effective stress tensor yields nonvanishing heat flux and anisotropic stress in a generic congruence. In the Ψ-comoving frame, the usual first-order thermodynamic identifications are recovered in invariant form, including K_JT_J=−Ψ̇/(κ^2Ψ) and η_J=Ψ̇/(2κ^2Ψ), with the bulk channel obtained in homogeneous and isotropic sectors. Thus, frame-invariant scalar-tensor thermodynamics is not intrinsically restricted to an Einstein-frame-like perfect-fluid description: it also admits a Jordan-frame-like invariant formulation in which the effective imperfect-fluid interpretation is manifest.
ER -