Thermodynamic structure of a generic null surface and the zeroth law in scalar-tensor theory

Abstract

We show that the equation of motion of scalar-tensor theory acquires thermodynamic identity when projected on a generic null surface. The relevant projection is given by $E_{ab}{l}^a{k}^b$, where $E_{ab}=8\pi T_{ab}^{(m)}$ represents the equation motion for gravitational field in presence of external matter, $l^a$ is the generator of the null surface and $k^a$ is the corresponding auxiliary null vector. Our analysis is done completely in a covariant way. Therefore all the thermodynamic quantities are in covariant form and hence can be used for any specific form of metric adapted to a null surface. We show this both in Einstein and Jordan frames and find that these two frames provide equivalent thermodynamic quantities. This is consistent with the previous findings for a Killing horizon. Also, a concrete proof of the zeroth law in scalar-tensor theory is provided when the null surface is defined by a Killing vector.

Typos corrected, published in Phys. Rev. D

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• Scalar fluid in scalar-tensor gravity from an equivalent picture of thermodynamic and fluid descriptions of gravitational dynamics
• Scalar-tensor theories of gravity from a thermodynamic viewpoint
• Boundary terms and Brown-York quasi-local parameters for scalar-tensor theory: a study on both timelike and null hypersurfaces
• Scalar-hairy Lovelock gravity respects zeroth law
• Lightlike singular hypersurfaces in quadratic gravity
• Possible fluid interpretation and tidal force equation on a generic null hypersurface in Einstein-Cartan theory
• Thermal nature of a generic null surface