From Osher Doctorow

M. O. Tahim, P. R. Landim, and C. A. S. Almeida (the latter has 25
papers in arXiv) in "Spacetime as a deformable solid", arXiv:
0705.4120 v1 [gr-qc] 28 May 2007 (the authors are at U. Federal do
Ceara Brazil) have argued that spacetime is a deformable solid.

They use the Landau-Raychaudhuri Equation for timelike or spacelike
curves, respectively:

1) d(theta)/d(tau) = -(1/3)theta^2 - u
2) d(theta)/d(lambda) = -(1/2)theta^2 - v

where u and v are each sums of two squares an an invariant related
respectively to distortions of volume and rotation of curves and
curvature, while theta is a scalar describing the expansion of volume.

From the viewpoint of Probable Influence/Causation, the equations (1)
and (2) are of special interest as generalizations of Riccati
Differential Equations:

3) dy/dt = A(t) + B(t)y + C(t)y^2

with B(t) = 0, which (3) is central to Probable Influence/Causation.

The Landau-Raychaudhuri Equation is common used to study and establish
spacetime singularities.

They prove the relationship between Einstein-Hilbert action and volume
deformation of a kind of "solid".

Osher Doctorow