SPHERICALLY SYMMETRIC SPACE–TIME WITH REGULAR DE SITTER CENTER

Abstract

We formulate the requirements which lead to the existence of a class of globally regular solutions of the minimally coupled GR equations asymptotically de Sitter at the center. The source term for this class, invariant under boosts in the radial direction, is classified as spherically symmetric vacuum with variable density and pressure [Formula: see text] associated with an r-dependent cosmological term [Formula: see text], whose asymptotic at the origin, dictated by the weak energy condition, is the Einstein cosmological term Λgμν, while asymptotic at infinity is de Sitter vacuum with λ < Λ or Minkowski vacuum. For this class of metrics the mass m defined by the standard ADM formula is related to both the de Sitter vacuum trapped at the origin and the breaking of space–time symmetry. In the case of the flat asymptotic, space–time symmetry changes smoothly from the de Sitter group at the center to the Lorentz group at infinity through radial boosts in between. Geometry is asymptotically de Sitter as r → 0 and asymptotically Schwarzschild at large r. In the range of masses m ≥ m crit , the de Sitter–Schwarzschild geometry describes a vacuum nonsingular black hole (ΛBH), and for m < m crit it describes G-lump — a vacuum selfgravitating particle-like structure without horizons. In the case of de Sitter asymptotic at infinity, geometry is asymptotically de Sitter as r → 0 and asymptotically Schwarzschild–de Sitter at large r. Λμν geometry describes, dependently on parameters m and [Formula: see text] and choice of coordinates, a vacuum nonsingular cosmological black hole, self-gravitating particle-like structure at the de Sitter background λgμν, and regular cosmological models with cosmological constant evolving smoothly from Λ to λ.