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A point mass in an isotropic universe: existence, uniqueness, and basic properties

REA Auditado

Criteria which a space-time must satisfy to represent a point mass embedded in an open Robertson-Walker (RW) universe are given. It is shown that McVittie’s solution in the case k=0 satisfies these criteria, but does not in the case k=-1. The existence of a solution for the case k=-1 is proven and its representation in terms of an elliptic integral is given.

Tema: general: 

• Ciencias›Matemáticas

Strengths of singularities in spherical symmetry

REA Auditado

Covariant equations characterizing the strength of a singularity in spherical symmetry are derived and several models are investigated. The difference between central and non-central singularities is emphasized. A slight modification to the definition of singularity strength is suggested. The gravitational weakness of shell crossing singularities in collapsing spherical dust is proven for timelike geodesics, closing a gap in the proof.

Tema: general: 

• Ciencias›Matemáticas

Central singularity in spherical collapse

REA Auditado

The gravitational strength of the central singularity in spherically symmetric space-times is investigated. Necessary conditions for the singularity to be gravitationally weak are derived and it is shown that these are violated in a wide variety of circumstances. These conditions allow conclusions to be drawn about the nature of the singularity without having to integrate the geodesic equations. In particular, any geodesic with a nonzero amount of angular momentum that impinges on the singularity terminates in a strong curvature singularity.

Tema: general: 

• Ciencias›Matemáticas

Naked singularities in cylindrical collapse of counterrotating dust shells

REA Auditado

Solutions describing the gravitational collapse of asymptotically flat cylindrical and prolate shells of (null) dust are shown to admit globally naked singularities.

Tema: general: 

• Ciencias›Matemáticas

Physical interpretation of gauge invariant perturbations of spherically symmetric space-times

REA Auditado

By calculating the Newman-Penrose Weyl tensor components of a perturbed spherically symmetric space-time with respect to invariantly defined classes of null tetrads, we give a physical interpretation, in terms of gravitational radiation, of odd parity gauge invariant metric perturbations. We point out how these gauge invariants may be used in setting boundary and/or initial conditions in perturbation theory.

Tema: general: 

• Ciencias›Matemáticas

Cauchy horizon stability in self-similar collapse: scalar radiation

REA Auditado

The stability of the Cauchy horizon in spherically symmetric self-similar collapse is studied by determining the flux of scalar radiation impinging on the horizon. This flux is found to be finite.

Tema: general: 

• Ciencias›Matemáticas

Role of anisotropy and inhomogeneity in Lemaitre-Tolman-Bondi collapse

REA Auditado

We study the effects of shear and density inhomogeneities in the formation of naked singularities in spherically symmetric dust space-times. We find that in general, complete knowledge of either one of these (time-dependent) functions, along with physically motivated boundary conditions, fully determines the entire space-time and consequently uniquely specifies the end-state of the gravitational collapse. In contrast–and of more physical relevance–we show that measurements of shear or density inhomogenity at an instant of time do not uniquely determine the outcome of the collapse.

Tema: general: 

• Ciencias›Matemáticas

Even perturbations of the self-similar Vaidya space-time

REA Auditado

We study even parity metric and matter perturbations of all angular modes in self-similar Vaidya space-time. We focus on the case where the background contains a naked singularity. Initial conditions are imposed, describing a finite perturbation emerging from the portion of flat space-time preceding the matter-filled region of space-time. The most general perturbation satisfying the initial conditions is allowed to impinge upon the Cauchy horizon (CH), where the perturbation remains finite: There is no “blue-sheet” instability.

Tema: general: 

• Ciencias›Matemáticas

Is the shell-focusing singularity of Szekeres space-time visible?

REA Auditado

The visibility of the shell-focusing singularity in Szekeres space-time—which represents quasispherical dust collapse—has been studied on numerous occasions in the context of the cosmic censorship conjecture. The various results derived have assumed that there exist radial null geodesics in the space-time. We show that such geodesics do not exist in general, and so previous results on the visibility of the singularity are not generally valid.

Tema: general: 

• Ciencias›Matemáticas

Gauge invariant perturbations of self-similar Lemaître-Tolman-Bondi spacetime: even parity modes with l≥2

REA Auditado

In this paper we consider gauge invariant linear perturbations of the metric and matter tensors describing the self-similar Lemaître-Tolman-Bondi (timelike dust) spacetime containing a naked singularity. We decompose the angular part of the perturbation in terms of spherical harmonics and perform a Mellin transform to reduce the perturbation equations to a set of ordinary differential equations with singular points. We fix initial data so the perturbation is finite on the axis and the past null cone of the singularity, and follow the perturbation modes up to the Cauchy horizon.

Tema: general: 

• Ciencias›Matemáticas