Effective General Relativistic Description of Jamming in Granular Matter

TL;DR

This paper introduces a novel approach to understanding jamming in granular matter by modeling grain dynamics within an effective curved spacetime, linking geometric properties to the onset of jamming.

Contribution

It proposes an effective general relativistic framework for granular jamming, unifying force balance symmetries and connecting to existing elasticity models.

Findings

Jamming corresponds to geodesic convergence in an effective curved space.

Trajectories twisting around each other negatively influence jamming.

The framework encompasses existing elasticity models within a linearized approximation.

Abstract

We propose here that certain observational features of granular matter in the infrared limit, exhibiting the phenomenon of {\it jamming}, arise from an underlying effective general relativistic description. The proposal stems from the assumption (which we justify on physical grounds) that grains in granular matter move freely in an {\it effective} curved Riemannian space. The termination of their trajectories at the onset of jamming is obtained from the focussing of a converging congruence of geodesics in such a space, as a solution of the Raychaudhuri equation for such congruences. This may happen irrespective of whether or not the curvature is sourced by external stresses (via an effective Einstein equation), although the properties of the resultant jammed state solution do differ in the two cases. A definite prediction of this geometrical approach is the negative role played by those trajectories which twist about each other, in reaching the jammed state. The local symmetries of granular interaction, translational and rotational invariance (corresponding to `force balance' and `torque balance' in standard force-based approaches to jamming) are inherent in the effective general relativity framework. A recently-proposed effective elasticity model of the jammed state, based on a tensorial variant of standard electrostatics (Vector Charge Theory), is seen to be entirely subsumed within the linearized version of the effective general relativistic description.