Abstract
We derive the gravitational equations of motion of general theories of gravity from thermodynamics applied to a local Rindler horizon through any point in spacetime. Specifically, for a given theory of gravity, we substitute the corresponding Wald entropy into the Clausius relation. Our approach works for all diffeomorphism-invariant theories of gravity in which the Lagrangian is a polynomial in the Riemann tensor.
Highlights
It has long been an attractive idea that gravity is not fundamental but, rather, emerges out of some more fundamental constituents
A more modern version of this is the gauge/gravity duality of string theory in which gravity is described by a gauge theory that lives in one dimension less; since the gauge theory does not itself contain the spacetime metric as a fundamental dynamical field, from this point of view, gravity is emergent
A great advance in the emergent gravity paradigm was made by Jacobson [1]
Summary
It has long been an attractive idea that gravity is not fundamental but, rather, emerges out of some more fundamental constituents. By assigning the thermodynamic properties of black hole horizons to local light-cones in spacetime (not necessarily near a black hole), the Einstein equation re-appears as an equation of state This seems to suggest that gravity arises in some thermodynamic approximation through the coarse-graining of some underlying microscopics. Our result suggests that classical gravitation always appears to have a quite intriguing thermodynamic origin This provides support for the idea that gravity might be emergent; it should be clarified that the sense in which the word “emergent” is used in the gravitational literature is weaker than in condensed matter: no properties of the microscopic theory are invoked here, and the only place where coarse-graining is indicated is in the Planckian units in which geometric entropy is defined
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