Einstein gravity as the thermal equilibrium state of a nonminimally coupled scalar field geometry

We test ideas of the recently proposed first-order thermodynamics of scalar-tensor gravity using an exact geometry sourced by a conformally coupled scalar field. We report a nonmonotonic behavior of the effective “temperature of gravity” not observed before and due to a new term in the equation describing the relaxation of gravity toward its state of equilibrium, i.e., Einstein gravity, showing a richer range of thermal behaviors of modified gravity than previously thought.

Figure 1

Evolution of $\mathcal{K}\mathcal{T}$ with the time $\tau$ (in units in which $r=1$ and $G=1$). The solid (purple) curve represents $\mathcal{K}\mathcal{T}(\tau ,1)$. The dashed vertical (orange) line marks the maximum value of $\mathcal{K}\mathcal{T}(\tau ,1)$.