Two Roads to the Null Energy Condition

TL;DR

This paper reveals that the null energy condition in general relativity originates from both matter-gravity interactions and thermodynamic principles, highlighting its fundamental dual nature.

Contribution

It demonstrates that the null energy condition arises from a geometric formulation in string theory and a thermodynamic perspective, challenging its traditional view as solely matter-related.

Findings

Null energy condition derived from Einstein's equations in string theory

Thermodynamic origin of the null energy condition established

Deep dual origins of gravity suggested

Abstract

The null energy condition has sweeping consequences in general relativity. I argue here that it has been misunderstood as a property exclusively of matter, when in fact it arises only in a theory of both matter and gravity. I then derive an equivalent geometric formulation of the null energy condition from worldsheet string theory, where it arises beautifully as simply Einstein's equations in two dimensions. But further, I show that this condition also has a thermodynamic origin, following from a local version of the second law of thermodynamics, applied to gravitational entropy. Thus, far from being an incidental property of matter, the validity of the null energy condition hints at the deep dual origins of gravity.