Einstein's Equations from the Stretched Future Light Cone

TL;DR

This paper derives Einstein's equations and their generalizations from thermodynamic principles applied to a novel geometric construct called the stretched future light cone, linking gravity and thermodynamics.

Contribution

It introduces the concept of the stretched future light cone and demonstrates deriving Einstein's equations from thermodynamics on this hypersurface, extending to broader gravity theories.

Findings

Einstein's equations can be derived from thermodynamics on the stretched future light cone.

The approach applies to a broad class of diffeomorphism-invariant gravity theories.

The derivation uses temperature and entropy attributed to the hypersurface.

Abstract

We define the stretched future light cone, a timelike hypersurface composed of the worldlines of radially accelerating observers with constant and uniform proper acceleration. By attributing temperature and entropy to this hypersurface, we derive Einstein's equations from the Clausius relation. Moreover, we show that the gravitational equations of motion for a broad class of diffeomorphism-invariant theories of gravity can be obtained from thermodynamics on the stretched future light cone, provided the Bekenstein-Hawking entropy is replaced by the Wald entropy.