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

TL;DR

This paper extends the thermodynamic derivation of gravity to non-commutative spacetime, deriving new Einstein equations without varying an action, thus suggesting gravity's emergent nature in a non-commutative context.

Contribution

It introduces a non-commutative version of the Raychaudhuri equation and derives non-commutative Einstein equations from thermodynamic principles.

Findings

Non-commutative Einstein equations derived from thermodynamics.

Spacetime thermodynamics applicable to non-commutative gravity.

No need for action variation in non-commutative gravity framework.

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.