D. S. Pereira, J. P. Mimoso
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 (FX/8πF)V⊥a, where Va≡hac∇c∇dXud and V⊥a denotes the component orthogonal to the four-acceleration aa. 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 qa=-K(DaTg+Tgaa) for all such configurations is possible if and only if FX(Φ,X)≡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 FX≠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 DaTg.
Keywords
General relativity / alternative theories of gravity
Physical Review D
Volume 113, Issue 084021
2026 April
