Deriving the gravitational field equation and horizon entropy for arbitrary diffeomorphism-invariant gravity from spacetime solid

TL;DR

This paper introduces a novel approach to derive gravitational field equations and horizon entropy for any diffeomorphism-invariant gravity theories by modeling spacetime as a solid with elasticity properties, linking entropy to spacetime deformation.

Contribution

It presents an alternative method to obtain gravity field equations and horizon entropy using spacetime solid analogy, extending the understanding of gravitational thermodynamics.

Findings

Derives field equations from an entropy extremization principle.

Shows Wald entropy arises from the spacetime solid model.

Applicable to arbitrary diffeomorphism-invariant gravity theories.

Abstract

Motivated by the analogy between the spacetime and the solid with inhomogeneous elasticity modulus, we present an alternative method to obtain the field equation of any diffeomorphism-invariant gravity, by extremizing the constructed entropy function of the displacement vector field of spacetime solid. In general stationary spacetimes, we show that the Wald entropy of horizon arises from the on-shell entropy function of spacetime solid.