Eckart heat-flux applicability in $F(\hat{I}¦,X)R$ theories and the existence of temperature gradients

Abstract

We show that in single--scalar theories of the form $\mathcal{L}=F(\hat{I}¦,X)R+G(\hat{I}¦,X)$, a generic nonminimal coupling $F(\hat{I}¦,X)$ induces, in the scalar--comoving frame, an additional transverse contribution to the effective heat flux, proportional to $(F_X/8\ddot{I}€F)V_{\perp a}$, where $V_a\equiv h_a{}^c{\nabla }_c{\nabla }_{d}X{u}^d$ and $V_{\perp a}$ 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 $F_X(\hat{I}¦,X)\equiv 0$, i.e.\ $F(\hat{I}¦,X)=F(\hat{I}¦)$, resulting in a theory that is a subclass of Horndeski. Thus, only Jordan--like theories of the type $F(\hat{I}¦)R+G(\hat{I}¦,X)$ admit a global Eckart fluid picture of the scalar sector, while models with $F_X\ne 0$ 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 $D_a{T}_g$.

10 pages. Matches published version

Cited by in corpus (1)

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