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

Cosmological term as a source of mass

In the spherically symmetric case the dominant energy condition together with the requirements of regularity at the center, asymptotic flatness and fineteness of the ADM mass, defines the family of asymptotically flat globally regular solutions to the Einstein minimally coupled equations which includes the class of metrics asymptotically de Sitter at approaching the regular center. The source term corresponds to an r-dependent cosmological term given by the second rank symmetric tensor invariant under boosts in the radial direction and evolving from de Sitter vacuum in the origin to Minkowski vacuum at infinity. Space-time symmetry changes smoothly from the de Sitter group at the center to the Lorentz group at infinity through the radial boosts in between. The standard formula for the ADM mass relates it to the de Sitter vacuum replacing a central singularity at the scale of symmetry restoration. For masses exceeding a certain critical value m_{crit} de Sitter-Schwarzschild geometry describes a vacuum nonsingular black hole, while beyond m_{crit} it describes a G-lump which is 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 to the Hawking temperature from the de Sitter horizon.Comment: 8 pages, revtex, 8 figures incorporated, to appear in Classical and Quantum Gravit

Spherically symmetric space-time with the regular de Sitter center

The requirements are formulated which lead to the existence of the class of globally regular solutions to the minimally coupled GR equations which are asymptotically de Sitter at the center. The brief review of the resulting geometry is presented. The source term, invariant under radial boots, is classified as spherically symmetric vacuum with variable density and pressure, associated with an r-dependent cosmological term, whose asymptotic in the origin, dictated by the weak energy condition, is the Einstein cosmological term. For this class of metrics the ADM mass 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. Dependently on mass, de Sitter-Schwarzschild geometry describes a vacuum nonsingular black hole, or G-lump - a vacuum selfgravitating particlelike structure without horizons. In the case of de Sitter asymptotic at infinity, geometry is asymptotically de Sitter at both origin and infinity and describes, dependently on parameters and choice of coordinates, a vacuum nonsingular cosmological black hole, selfgravitating particlelike structure at the de Sitter background and regular cosmological models with smoothly evolving vacuum energy density.Comment: Latex, 10 figures, extended version of the plenary talk at V Friedmann Intern. Conf. on Gravitation and Cosmology, Brazil 2002, to appear in Int.J.Mod.Phys.

Quantum Radiation of Oscillons

Many classical scalar field theories possess remarkable solutions: coherently oscillating, localized clumps, known as oscillons. In many cases, the decay rate of classical small amplitude oscillons is known to be exponentially suppressed and so they are extremely long lived. In this work we compute the decay rate of quantized oscillons. We find it to be a power law in the amplitude and couplings of the theory. Therefore, the quantum decay rate is very different to the classical decay rate and is often dominant. We show that essentially all oscillons eventually decay by producing outgoing radiation. In single field theories the outgoing radiation has typically linear growth, while if the oscillon is coupled to other bosons the outgoing radiation can have exponential growth. The latter is a form of parametric resonance: explosive energy transfer from a localized clump into daughter fields. This may lead to interesting phenomenology in the early universe. Our results are obtained from a perturbative analysis, a non-perturbative Floquet analysis, and numerics.Comment: 16 pages, 6 figures. V2: Expanded sections 1 and 2 plus other minor changes, added references. V3: Updated to resemble version published in Phys. Rev. D. V4: Slight rewording in 2nd paragrap

Dynamics and Non-Gaussianity in the Weak-Dissipative Warm Inflation Scenario

We calculate the general solutions for a warm inflationary scenario with weak dissipation, reviewing the dissipative dynamics of the two-fluid system, and calculate the bispectrum of the gravitational field fluctuations generated in the case where dissipation of the vacuum potential during inflation is the mechanism for structure formation, but is the sub-dominant effect in the dynamics of the scalar field during slow-roll. The bispectrum is non-zero because of the self-interaction of the scalar field. We compare the predictions with both those of standard, or `supercooled', inflationary models, and warm inflation models with strong dissipation and consider the detectability of these levels of non-Gaussianity in the bispectrum of the cosmic microwave background. We find that the levels of non--Gaussianity for warm and supercooled inflation are an order of magnitude different.Comment: Replaced with version accepted for publication in Phys. Rev. D., minor changes; 7 pages, Late

Nonsingular vacuum cosmologies with a variable cosmological term

We present nonsingular cosmological models with a variable cosmological term described by the second-rank symmetric tensor $\Lambda_{mn}$ evolving from $\Lambda g_{mn}$ to $\lambda g_{mn}$ with $\lambda < \Lambda$. All $\Lambda_{mn}$ dominated cosmologies belong to Lemaitre type models for an anisotropic perfect fluid. The expansion starts from a nonsingular nonsimultaneous de Sitter bang, with $\Lambda$ on the scale responsible for the earliest accelerated expansion, which is followed by an anisotropic Kasner type stage. For a certain class of observers these models can be also identified as Kantowski-Sachs models with regular R regions. For Kantowski-Sachs observers the cosmological evolution starts from horizons with a highly anisotropic ``null bang'' where the volume of the spatial section vanishes. We study in detail the spherically symmetric case and consider the general features of cosmologies with planar and pseudospherical symmetries. Nonsingular $\Lambda_{mn}$ dominated cosmologies are Bianchi type I in the planar case and hyperbolic analogs of the Kantowski-Sachs models in the pseudospherical case. At late times all models approach a de Sitter asymptotic with small $\lambda$.Comment: revtex, 10 pages, 8 eps figure