Vacuum nonsingular black hole

Abstract

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 → 0, describes a vacuum nonsingular 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 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 ρ(r) = ρ0e −r 3 /r 2 0 rg where ρ0 is the density of de Sitter vacuum at the center, r0 = 3/κρ0 is de Sitter radius and rg is the Schwarzschild radius.

Family of regular interiors for nonrotating black holes withT00=T11

“…(52), we get that R = λR Twopowers , with .84 < λ < 1.34, for any N. Therefore, R is again of the same order of magnitude, despite the differences in the choice of the profile of the energy density and of the tangential pressures. Comparing now the model proposed here with the original one in [20], we see that both yield similar conclusions (in the instances they can be compared). For example, in the mentioned work, a characteristic radius was found for the collapsed body.…”

“…As we are dealing with spacetimes which are spherically symmetric, a natural generalization is to assume that the body may be described by a solution which is invariant to any non-rotating observer, with a free radial motion, instead of a solution which is invariant to any observer. This generalization of the energy-matter content of the body is called spherically symmetric quantum vacuum (SSQV), after [20] -see also [22]-and requires the imposition of T 0 0 = T 1 1 , for any non-rotating observer. This is the type of enery-matter content that is considered in [18]- [29] and will be the one used in the first part of this work, until we get to Sect.…”

“…Two constitute the well-known proposals of [18,19,44] and [20,21]. Two more come from a proposal in [23]- [26], for electrically charged bodies, and the proposal given in [29], for magnetically charged ones.…”

“…Some time after the appearance of the previous cases a new model for a regular interior of a non-charged BH was proposed [20]. However the approach was now quite different to that of the previous authors.…”

“…In all these cases considered so far, either no distinction has been made between the interior and the exterior of the body (see e.g., [20]- [26]) or there appears a singular distribution of matter at the surface of the body (see e.g. [18,19]).…”