What drives the time evolution of the spacetime geometry?

TL;DR

This paper presents a thermodynamic perspective on spacetime evolution, showing that deviations from holographic equipartition drive the dynamics of the gravitational field, aligning with Einstein's equations.

Contribution

It introduces a thermodynamic framework linking the rate of change of gravitational momentum to degrees of freedom differences, offering a holographic interpretation of spacetime evolution.

Findings

In static spacetimes, bulk and boundary degrees of freedom are equal.

Departure from holographic equipartition drives spacetime evolution.

The approach reproduces Einstein's equations from a thermodynamic perspective.

Abstract

I show that in a general, evolving spacetime, the rate of change of gravitational momentum is related to the difference between the number of degrees of freedom in the bulk and the boundary of a region. This expresses the gravitational field equation in the thermodynamic language which is the natural description, if gravity is an emergent phenomenon. In all static spacetimes, the number of degrees of freedom in the boundary is equal to the number of degrees of freedom in the bulk; i.e., these spacetimes maintain holographic equipartition. It is the departure from holographic equipartition that drives the time evolution of the spacetime. This result, which is equivalent to Einstein's equations, provides an elegant, holographic, description of spacetime dynamics.