Eckart heat-flux applicability in $F(Φ,X)R$ theories and the existence of temperature gradients

David S. Pereira; José Pedro Mimoso

doi:10.1103/z92y-sp66

paper

Eckart heat-flux applicability in $F (Φ, X) R$ theories and the existence of temperature gradients

arXiv:2512.20553 · doi:10.1103/z92y-sp66

Abstract

We show that in single--scalar theories of the form $L = F (Φ, X) R + G (Φ, X)$ , a generic nonminimal coupling $F (Φ, X)$ induces, in the scalar--comoving frame, an additional transverse contribution to the effective heat flux, proportional to $(F_{X} /8 π F) V_{⊥ a}$ , where $V_{a} \equiv h_{a}^{c} \nabla_{c} \nabla_{d} X u^{d}$ and $V_{⊥ a}$ denotes the component orthogonal to the 4--acceleration $a_{a}$ . This term cannot in general be written as a spatial temperature gradient, and therefore obstructs a standard Eckart interpretation of the scalar sector for arbitrary timelike scalar configurations. As a result, requiring an Eckart heat flux $q_{a} = - K (D_{a} T_{g} + T_{g} a_{a})$ for all such configurations is possible if and only if $F_{X} (Φ, X) \equiv 0$ , i.e.\ $F (Φ, X) = F (Φ)$ , resulting in a theory that is a subclass of Horndeski. Thus, only Jordan--like theories of the type $F (Φ) R + G (Φ, X)$ admit a global Eckart fluid picture of the scalar sector, while models with $F_{X} \neq = 0$ can recover an Eckart--like form only on highly symmetric backgrounds where the transverse contribution vanishes or collapses to a single gradient direction. We also make a brief comment on the existence of temperature gradients $D_{a} T_{g}$ .

arXiv comment10 pages. Matches published version

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Thermal channels of scalar and tensor waves in Jordan-frame scalar--tensor gravity

Eckart heat-flux applicability in F(Φ,X)R theories and the existence of temperature gradients

Abstract

References in corpus (51)

Cited by in corpus (1)

Eckart heat-flux applicability in $F (Φ, X) R$ theories and the existence of temperature gradients