Recovering semiclassical Einstein's equation using generalized entropy

TL;DR

This paper demonstrates that the semiclassical Einstein's equation can be derived from generalized entropy without relying on entanglement equilibrium assumptions, supporting the validity of the semiclassical approximation.

Contribution

It introduces a novel thermodynamic approach using generalized entropy to recover the semiclassical Einstein's equation without entanglement assumptions.

Findings

Successfully derives Einstein's equation from generalized entropy

Shows the approach does not depend on entanglement equilibrium

Validates the semiclassical approximation for gravity

Abstract

In this letter, we show that the Semiclassical Einstein's Field Equation can be recovered using the generalized entropy $S_{gen}$. This approach is reminiscent of non-equilibrium thermodynamics. Furthermore, contrary to the entanglement equilibrium approach of deriving the semiclassical Einstein's equation, this approach does not require any such assumptions and still recovers its correct form. Therefore, in a sense, we also show the validity of the semiclassical approximation, a crucial approach for establishing a number of important ideas such as the Hawking effect.