General relativity involves an inhomogeneous metric field that causally depends on the distribution of matter, contradicting Helmholtz's presupposition of metric homogeneity

Considering the general case of \(n\) dimensions, and using Lie groups and Lie algebras, Sophus Lie, (Lie (1886/1935, 1890a,b)), later developed and improved Helmholtz’s justification. However, the Helmholtz-Lie treatment of, and solution to, the problem of space, lost its relevance with the arrival of Einstein’s theory of general relativity. As Weyl (1922b) points out, instead of a three-dimensional continuum we must now consider a four-dimensional continuum, the metric of which is not p