Abstract
A set of new exact analytical general relativity (GR) solutions with time-dependent and spatially inhomogeneous quintessence demonstrate (1) a static non-empty space–time with a horizon-type singular surface; (2) time-dependent spatially homogeneous ‘spheres’ which are completely different in geometry from the Friedmann isotropic models; (3) infinitely strong anti-gravity at a ‘true’ singularity where the density is infinitely large. It is also found that (4) the GR solutions allow for an extreme ‘density-free’ form of energy that can generate regular space–time geometries.
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