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2016

Higher derivative gravity: field equation as the equation of state

Dey, Ramit, Liberati, Stefano, Mohd, Arif

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One of the striking features of general relativity is that the Einstein equation is implied by the Clausius relation imposed on a small patch of locally constructed causal horizon.

Extension of this thermodynamic derivation of the field equation to more general theories of gravity has been attempted many times in the last two decades.
In particular, equations of motion for minimally coupled higher curvature theories of gravity, but without the derivatives of curvature, have previously been derived using a thermodynamic reasoning.
In that derivation the horizon slices were endowed with an entropy density whose form resembles that of the Noether charge for diffeomorphisms, and was dubbed the Noetheresque entropy.

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Then

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