Crystal gravity

TL;DR

This paper explores a novel concept called 'crystal gravity,' where solid matter's spontaneous symmetry breaking influences spacetime structure, drawing parallels with Higgs phenomena in gauge theories and examining its implications within a stationary framework.

Contribution

It introduces the idea of 'crystal gravity' as a Higgs-like phase of gravity, connecting elasticity theory with general relativity through a geometrical formulation.

Findings

Elasticity theory relates to spacetime symmetry breaking.

Geometrical formulation simplifies the marriage of elasticity and gravity.

Stationary 'Higgsed gravity' exhibits rich and simple physical phenomena.

Abstract

We address a subject that could have been analyzed century ago: how does the universe of general relativity look like when it would have been filled with solid matter? Solids break spontaneously the translations and rotations of space itself. Only rather recently it was realized in various context that the order parameter of the solid has a relation to Einsteins dynamical space time which is similar to the role of a Higgs field in a Yang-Mills gauge theory. Such a "crystal gravity" is therefore like the Higgs phase of gravity. The usual Higgs phases are characterized by a special phenomenology. A case in point is superconductivity exhibiting phenomena like the Type II phase, characterized by the emergence of an Abrikosov lattice of quantized magnetic fluxes absorbing the external magnetic field. What to expect in the gravitational setting? The theory of elasticity is the universal effective field theory associated with the breaking of space translations and rotations having a similar status as the phase action describing a neutral superfluid. A geometrical formulation appeared in its long history, similar in structure to general relativity, which greatly facilitates the marriage of both theories. With as main limitation that we focus entirely on stationary circumstances -- the dynamical theory is greatly complicated by the lack of Lorentz invariance -- we will present a first exploration of a remarkably rich and often simple physics of "Higgsed gravity".