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

Effective General Relativistic Description of Jamming in Granular Matter