Non-commutative Gravity and the Einstein-Van der Waals Equation of State

Abstract

A calculation by Jacobson [1] strongly implies that the field equations which describe gravity are emergent phenomena. In this paper, the method is extended to the case of a non-commutative spacetime. By making use of a non-commutative version of the Raychaudhuri equation, a new set of non-commutative Einstein equations is derived. The results demonstrate that it is possible to use spacetime thermodynamics to work with non-commutative gravity without the need to vary a non-commutative action.