The cosmological term as a source of mass

Abstract

In the spherically symmetric case the dominant energy condition, together with the requirement of regularity at the center, asymptotic flatness and finiteness of the ADM mass, defines the family of asymptotically flat globally regular solutions to the Einstein equations which includes the class of metrics asymptotically de Sitter as r → 0. The source term corresponds to an r−dependent cosmological term Λµν invariant under boosts in the radial direction and evolving from the de Sitter vacuum Λgµν in the origin to the Minkowski vacuum at infinity. The ADM mass is related to cosmological term by m = (2G) −1 ∞ 0 Λ t t r 2 dr, with de Sitter vacuum replacing a central singularity at the scale of symmetry restoration. Space-time symmetry changes smoothly from the de Sitter group near the center to the Lorentz group at infinity through radial boosts in between. 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. Quantum energy spectrum of G-lump is shifted down by the binding energy, and zero-point vacuum mode is fixed at the value corresponding (up to the coefficient) to the Hawking temperature from the de Sitter horizon.

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].…”

“…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]. Mass of a compact object is generically related to interior de Sitter vacuum and to breaking of space-time symmetry from the de Sitter group in the origin [65,77,79].…”

“…In the asymptotically flat case, the metric is asymptotically de Sitter for r → 0 and asymptotically Schwarzschild for large r. It has two horizons which coincide for a certain mass M cr corresponding to an extreme black hole [65,80]. Typical behavior of the metric function is shown in Figure 2 It evaporates from both horizons, and generic asymptotic behavior of the metric function g(r) defines dynamics of evaporation.…”

A cyclic universe with colour fields

“…There exists also observational evidence [50][51][52] suggesting that our universe in the past was contracted to a very small volume, which is regarded by the standard cosmological model as an indication that the universe could be born from a singularity. On the other hand, singularities could, in principle, be avoided by relaxing the conditions required by the singularities theorems [48,49]. For example, within the classical framework of Einstein-Cartan theory [53][54][55][56][57][58], torsion contributing to the energy-momentum tensor leads to an effective negative pressure and eliminates the singularity.…”