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

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.

19 pages, no figure, to be published in Phys. Rev. D

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• LCDM Model in f(T) Gravity: Reconstruction, Thermodynamics and Stability
• Thermodynamic properties of modified gravity theories
• Finite entanglement entropy from the zero-point-area of spacetime
• The emergence of gauge invariance: the stay-at-home gauge versus local-global duality
• Quantum computational complexity, Einstein's equations and accelerated expansion of the Universe
• Thermodynamics in Little Rip cosmology in the framework of a type of f(R,T) gravity
• Modified gravity from an entropy functional