Spherically Symmetric Space–time With Regular De Sitter Center

Abstract

The requirements are formulated which lead to the existence of the class of globally regular solutions to the minimally coupled GR equations asymptotically de Sitter at the center. 1 The source term for this class, invariant under boosts in the radial direction, is classified as spherically symmetric vacuum with variable density and pressure T vac µν associated with an r−dependent cosmological term Λµν = 8πGT vac µν , whose asymptotic in 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 de Sitter vacuum trapped in the origin and to 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 ≥ mcrit, de Sitter-Schwarzschild geometry describes a vacuum nonsingular black hole (ΛBH), and for m < mcrit it describes G-lump -a vacuum selfgravitating particlelike 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 q = Λ/λ and choice of coordinates, a vacuum nonsingular cosmological black hole, selfgravitating particlelike structure at the de Sitter background λgµν, and regular cosmological models with cosmological constant evolving smoothly from Λ to λ.

Slowly rotating supercompact Schwarzschild stars

“…Some alternatives to black holes have been proposed [22,27,30,53]. In particular, In the gravastar model, the spacetime suffers a quantum phase transition, which leads to p = − , starting at the center of the star and moving outwards thus releasing huge amounts of energy and entropy [63].…”

Thermodynamics of Regular Cosmological Black Holes with the de Sitter Interior

“…On the other hand, the Einstein equations admit the class of regular spherically symmetric solutions asymptotically de Sitter at both the origin and infinity [64][65][66]. It was found by investigation of typical features of spherically symmetric solutions to the Einstein equations.…”

“…where ρ(r) = T A stress-energy tensor specified by (9) and satisfying the weak energy condition (non-zero density for any observer on a time-like curve) represents a spherically symmetric anisotropic (see (10)) vacuum fluid [54,[64][65][66][67]70,71] whose symmetry is reduced as compared with the maximally symmetric de Sitter vacuum [72]. Vacuum with a reduced symmetry (for a review see [73][74][75][76][77][78][79]) provides a unified description of dark ingredients in the Universe by a vacuum dark fluid [67,71], which represents distributed vacuum dark energy by a time evolving and spatially inhomogeneous cosmological term [64], and compact objects with de Sitter vacuum interior: regular black holes and gravitational vacuum solitons G-lumps [65,67] which are regular gravitationally bound vacuum structures without horizons (dark particles or dark stars, dependently on a mass) [65,80,81].…”

Generic Features of Thermodynamics of Horizons in Regular Spherical Space-Times of the Kerr-Schild Class

“…Stress-energy tensors responsible for the Kerr-Schild metrics have the algebraic structure [20][21][22][23] T t t = T r r (p r = −ρ) (2) and can be identified as vacuum dark fluid defined by the algebraic structure of its stress-energy tensor [24]. The Einstein cosmological term λδ µ ν , λ = const, corresponds to the maximally symmetric de Sitter vacuum T µ ν = ρ vac δ µ ν ; ρ vac = (8πG) −1 λ = const.…”