Irina Dymnikova

Vacuum nonsingular black hole

The spherically symmetric vacuum stress-energy tensor with one assumption concerning its specific form generates the exact analytic solution of the Einstein equations which for larger coincides with the Schwarzschild solution, for smallr behaves like the de Sitter solution and describes a spherically symmetric black hole singularity free everywhere.

The cosmological term as a source of mass

In the spherically symmetric case, the dominant energy condition, together with the requirement of regularity at the centre, 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 ??? invariant under boosts in the radial direction and evolving from the de Sitter vacuum ?g?? in the origin to the Minkowski vacuum at infinity. The ADM mass is related to a cosmological term by m = (2G)?1?0??ttr2 dr, with the de Sitter vacuum replacing a central singularity at the scale of symmetry restoration. Spacetime symmetry changes smoothly from the de Sitter group near the centre 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 (?BH), and for m < mcrit, it describes a G-lump?a vacuum self-gravitating particle-like structure without horizons. The quantum energy spectrum of the 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.

Regular electrically charged vacuum structures with de Sitter centre in nonlinear electrodynamics coupled to general relativity

We address the question of existence of regular spherically symmetric electrically charged solutions in nonlinear electrodynamics (NED) coupled to general relativity. The stress-energy tensor of the electromagnetic field has the algebraic structure T 0 0 = T 1 1 . In this case, the weak energy condition leads to the de Sitter asymptotic on approaching a regular centre. In the de Sitter centre of an electrically charged NED structure, electric field, geometry and stress-energy tensor are regular without the Maxwell limit which is replaced by the de Sitter limit: energy density of a field is maximal and gives an effective cut-off on self-energy density, produced by NED coupled to gravity and related to the cosmological constant A. Regular electric solutions, satisfying WEC, suffer from one cusp in the Lagrangian £(F), which creates the problem in an effective geometry whose geodesics are world lines of NED photons. We investigate propagation of photons and show that their world lines never terminate which suggests absence of singularities in the effective geometry. To illustrate these results we present the particular example of the new exact analytic spherically symmetric electrically charged solution with the de Sitter centre.

Spherically symmetric space-time with the regular de Sitter center

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 associated with an r-dependent cosmological term , 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 ≥ mcrit, the de Sitter–Schwarzschild geometry describes a vacuum nonsingular black hole (ΛBH), and for m < mcrit 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 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.

The algebraic structure of a cosmological term in spherically symmetric solutions

Abstract We propose to describe the dynamics of a cosmological term in the spherically symmetric case by an r -dependent second rank symmetric tensor Λ μν invariant under boosts in the radial direction. This proposal is based on the Petrov classification scheme and Einstein field equations in the spherically symmetric case. The inflationary equation of state p =− ρ is satisfied by the radial pressure, p r Λ =− ρ Λ . The tangential pressure p ⊥ Λ is calculated from the conservation equation Λ μ ν ; μ =0.

DE SITTER-SCHWARZSCHILD BLACK HOLE: ITS PARTICLELIKE CORE AND THERMODYNAMICAL PROPERTIES

We analyze the globally regular solution of the Einstein equations describing a black hole whose singularity is replaced by the de Sitter core. The de Sitter—Schwarzschild black hole (SSBH) has two horizons. Inside of it there exists a particlelike structure hidden under the external horizon. The critical value of mass parameter Mcr1 exists corresponding to the degenerate horizon. It represents the lower limit for a black-hole mass. Below Mcr1 there is no black hole, and the de Sitter-Schwarzschild solution describes a recovered particlelike structure. We calculate the Hawking temperature of SSBH and show that specific heat is broken and changes its sign at the value of mass Mcr2>Mcr1 which means that a second-order phase transition occurs at that point. We show that the Hawking temperature drops to zero when a mass approaches the lower limit Mcr1.

Stability of a vacuum non-singular black hole

This is the first of series of papers in which we investigate stability of the spherically symmetric spacetime with de Sitter centre. Geometry, asymptotically Schwarzschild for large r and asymptotically de Sitter as r → 0, describes a vacuum non-singular black hole for m ≥ mcr and particle-like self-gravitating structure for m < mcr where a critical value mcr depends on the scale of the symmetry restoration to the de Sitter group in the origin. In this paper, we address the question of stability of a vacuum non-singular black hole with de Sitter centre to external perturbations. We specify first two types of geometries with and without changes of topology. Then we derive the general equations governing polar perturbations, specify criteria of stability for a regular black hole with de Sitter centre, and study in detail the case of the density profile where ρ0 is the density of de Sitter vacuum at the centre, is the de Sitter radius and rg is the Schwarzschild radius.

Regular rotating electrically charged black holes and solitons in non-linear electrodynamics minimally coupled to gravity

In non-linear electrodynamics coupled to gravity, regular spherically symmetric electrically charged solutions satisfy the weak energy condition and have an obligatory de Sitter center. By the Gurses–Gursey algorithm they are transformed to spinning electrically charged solutions that are asymptotically Kerr–Newman for a distant observer. Rotation transforms the de Sitter center into a de Sitter vacuum surface which contains the equatorial disk r = 0 as a bridge. We present a general analysis of the horizons, ergoregions and de Sitter surfaces, as well as the conditions of the existence of regular solutions to the field equations. We find asymptotic solutions and show that de Sitter vacuum surfaces have properties of a perfect conductor and ideal diamagnetic, violation of the weak energy condition is prevented by the basic requirement of electrodynamics of continued media, and the Kerr ring singularity is replaced with the superconducting current.

DECAY OF COSMOLOGICAL CONSTANT AS BOSE CONDENSATE EVAPORATION

We consider the process of decay of symmetric vacuum state as evaporation of a Bose condensate of physical Higgs particles, defined over asymmetric vacuum state. Energy density of their selfinteraction is identified with cosmological constant

Universes inside a Λ black hole

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