Gravity as elasticity of spacetime: a paradigm to understand horizon thermodynamics and cosmological constant

TL;DR

This paper proposes a paradigm where spacetime behaves like an elastic solid, explaining horizon thermodynamics and addressing the cosmological constant problem through microscopic degrees of freedom and their surface contributions.

Contribution

It introduces a novel interpretation of spacetime as an elastic solid, deriving Einstein's equations from microscopic microstructure and explaining horizon entropy and the cosmological constant.

Findings

Horizon entropy is a surface contribution proportional to area.

Einstein's equations emerge as a consistency condition of the spacetime microstructure.

Vacuum energy response leads to a near cancellation of the cosmological constant.

Abstract

It is very likely that the quantum description of spacetime is quite different from what we perceive at large scales, $l\gg (G\hbar/c^3)^{1/2}$. The long wave length description of spacetime, based on Einstein's equations, is similar to the description of a continuum solid made of a large number of microscopic degrees of freedom. This paradigm provides a novel interpretation of coordinate transformations as deformations of "spacetime solid" and allows one to obtain Einstein's equations as a consistency condition in the long wavelength limit. The entropy contributed by the microscopic degrees of freedom reduces to a pure surface contribution when Einstein's equations are satisfied. The horizons arises as "defects" in the "spacetime solid" (in the sense of well defined singular points) and contributes an entropy which is one quarter of the horizon area. Finally, the response of the microstructure to vacuum energy leads to a near cancellation of the cosmological constant, leaving behind a tiny fluctuation which matches with the observed value.