  In the spherically symmetric case the requirements of regularity of density
and pressures and finiteness of the ADM mass $m$, together with the weak energy
condition, define the family of asymptotically flat globally regular solutions
to the Einstein minimally coupled equations which includes the class of metrics
asymptotically de Sitter as $r\to 0$. A source term connects smoothly de Sitter
vacuum in the origin with the Minkowski vacuum at infinity and corresponds to
anisotropic vacuum defined macroscopically by the algebraic structure of its
stress-energy tensor invariant under boosts in the radial direction.
Dependently on parameters, geometry describes vacuum nonsingular black holes,
and self-gravitating particle-like structures whose ADM mass is related to both
de Sitter vacuum trapped in the origin and smooth breaking of space-time
symmetry. The geometry with the regular de Sitter center has been applied to
estimate geometrical limits on sizes of fundamental particles, and to evaluate
the gravito-electroweak unification scale from the measured mass-squared
differences for neutrino.
