Stability of a vacuum nonsingular black hole

This is the first of series of papers in which we investigate stability of the spherically symmetric space-time with de Sitter center. Geometry, asymptotically Schwarzschild for large $r$ and asymptotically de Sitter as $r\to 0$, describes a vacuum nonsingular black hole for $m\geq m_{cr}$ and particle-like self-gravitating structure for $m < m_{cr}$ where a critical value $m_{cr}$ depends on the scale of the symmetry restoration to 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 center to external perturbations. We specify first two types of geometries with and without changes of topology. Then we derive the general equations for an arbitrary density profile and show that in the whole range of the mass parameter $m$ objects described by geometries with de Sitter center remain stable under axial perturbations. In the case of the polar perturbations we find criteria of stability and study in detail the case of the density profile $\rho(r)=\rho_0 e^{-r^3/r_0^2 r_g}$ where $\rho_0$ is the density of de Sitter vacuum at the center, $r_0$ is de Sitter radius and $r_g$ is the Schwarzschild radius.Comment: 18 pages, 8 figures, submitted to "Classical and Quantum Gravity

Gravastars must have anisotropic pressures

One of the very small number of serious alternatives to the usual concept of an astrophysical black hole is the "gravastar" model developed by Mazur and Mottola; and a related phase-transition model due to Laughlin et al. We consider a generalized class of similar models that exhibit continuous pressure -- without the presence of infinitesimally thin shells. By considering the usual TOV equation for static solutions with negative central pressure, we find that gravastars cannot be perfect fluids -- anisotropic pressures in the "crust" of a gravastar-like object are unavoidable. The anisotropic TOV equation can then be used to bound the pressure anisotropy. The transverse stresses that support a gravastar permit a higher compactness than is given by the Buchdahl--Bondi bound for perfect fluid stars. Finally we comment on the qualitative features of the equation of state that gravastar material must have if it is to do the desired job of preventing horizon formation.Comment: V1: 15 pages; 4 figures; uses iopart.cls; V2: 16 pages; added 3 references and brief discussio

Multihorizon spherically symmetric spacetimes with several scales of vacuum energy

We present a family of spherically symmetric multihorizon spacetimes with a vacuum dark fluid, associated with a time-dependent and spatially inhomogeneous cosmological term. The vacuum dark fluid is defined in a model-independent way by the symmetry of its stressenergy tensor, i.e. its invariance under Lorentz boosts in a distinguished spatial direction (p r = ρ for the spherically symmetric fluid), which makes dark fluid essentially anisotropic and allows its density to evolve. The related cosmological models belong to the Lemaître class of models with anisotropic fluids and describe evolution of a universe with several scales of vacuum energy related to phase transitions during its evolution. The typical behavior of solutions and the number of spacetime horizons are determined by the number of vacuum scales. We study in detail the model with three vacuum scales: GUT, QCD and that responsible for the present accelerated expansion. The model parameters are fixed by the observational data and by conditions of analyticity and causality. We find that our Universe has three horizons. During the first inflation, the Universe enters a T-region, which makes expansion irreversible. After second phase transition at the QCD scale, the Universe enters R-region, where for a long time its geometry remains almost pseudo-Euclidean. After crossing the third horizon related to the present vacuum density, the Universe should have to enter the next T-region with the inevitable expansion. © 2012 IOP Publishing Ltd