755 research outputs found

### Timelike and null focusing singularities in spherical symmetry: a solution to the cosmological horizon problem and a challenge to the cosmic censorship hypothesis

Extending the study of spherically symmetric metrics satisfying the dominant
energy condition and exhibiting singularities of power-law type initiated in
SI93, we identify two classes of peculiar interest: focusing timelike
singularity solutions with the stress-energy tensor of a radiative perfect
fluid (equation of state: $p={1\over 3} \rho$) and a set of null singularity
classes verifying identical properties. We consider two important applications
of these results: to cosmology, as regards the possibility of solving the
horizon problem with no need to resort to any inflationary scenario, and to the
Strong Cosmic Censorship Hypothesis to which we propose a class of physically
consistent counter-examples.Comment: 26 pages, 2 figures, LaTeX file. Submitted to Phys. Rev.

### Newtonian and Post-Newtonian approximations of the k = 0 Friedmann Robertson Walker Cosmology

In a previous paper we derived a post-Newtonian approximation to cosmology
which, in contrast to former Newtonian and post-Newtonian cosmological
theories, has a well-posed initial value problem. In this paper, this new
post-Newtonian theory is compared with the fully general relativistic theory,
in the context of the k = 0 Friedmann Robertson Walker cosmologies. It is found
that the post-Newtonian theory reproduces the results of its general
relativistic counterpart, whilst the Newtonian theory does not.Comment: 11 pages, Latex, corrected typo

### Simple Analytic Models of Gravitational Collapse

Most general relativity textbooks devote considerable space to the simplest
example of a black hole containing a singularity, the Schwarzschild geometry.
However only a few discuss the dynamical process of gravitational collapse, by
which black holes and singularities form. We present here two types of analytic
models for this process, which we believe are the simplest available; the first
involves collapsing spherical shells of light, analyzed mainly in
Eddington-Finkelstein coordinates; the second involves collapsing spheres
filled with a perfect fluid, analyzed mainly in Painleve-Gullstrand
coordinates. Our main goal is pedagogical simplicity and algebraic
completeness, but we also present some results that we believe are new, such as
the collapse of a light shell in Kruskal-Szekeres coordinates.Comment: Submitted to American Journal of Physic

### Falloff of the Weyl scalars in binary black hole spacetimes

The peeling theorem of general relativity predicts that the Weyl curvature
scalars Psi_n (n=0...4), when constructed from a suitable null tetrad in an
asymptotically flat spacetime, fall off asymptotically as r^(n-5) along
outgoing radial null geodesics. This leads to the interpretation of Psi_4 as
outgoing gravitational radiation at large distances from the source. We have
performed numerical simulations in full general relativity of a binary black
hole inspiral and merger, and have computed the Weyl scalars in the standard
tetrad used in numerical relativity. In contrast with previous results, we
observe that all the Weyl scalars fall off according to the predictions of the
theorem.Comment: 7 pages, 3 figures, published versio

### Shear-Free Gravitational Waves in an Anisotropic Universe

We study gravitational waves propagating through an anisotropic Bianchi I
dust-filled universe (containing the Einstein-de-Sitter universe as a special
case). The waves are modeled as small perturbations of this background
cosmological model and we choose a family of null hypersurfaces in this
space-time to act as the histories of the wavefronts of the radiation. We find
that the perturbations we generate can describe pure gravitational radiation if
and only if the null hypersurfaces are shear-free. We calculate the
gauge-invariant small perturbations explicitly in this case. How these differ
from the corresponding perturbations when the background space-time is
isotropic is clearly exhibited.Comment: 32 pages, accepted for publication in Physical Review

### Operational significance of the deviation equation in relativistic geodesy

Deviation equation: Second order differential equation for the 4-vector which
measures the distance between reference points on neighboring world lines in
spacetime manifolds.
Relativistic geodesy: Science representing the Earth (or any planet),
including the measurement of its gravitational field, in a four-dimensional
curved spacetime using differential-geometric methods in the framework of
Einstein's theory of gravitation (General Relativity).Comment: 9 pages, 4 figures, contribution to the "Encyclopedia of Geodesy".
arXiv admin note: text overlap with arXiv:1811.1047

### Post-Newtonian Cosmology

Newtonian Cosmology is commonly used in astrophysical problems, because of
its obvious simplicity when compared with general relativity. However it has
inherent difficulties, the most obvious of which is the non-existence of a
well-posed initial value problem. In this paper we investigate how far these
problems are met by using the post-Newtonian approximation in cosmology.Comment: 12 pages, Late

### You Can't Get Through Szekeres Wormholes - or - Regularity, Topology and Causality in Quasi-Spherical Szekeres Models

The spherically symmetric dust model of Lemaitre-Tolman can describe
wormholes, but the causal communication between the two asymptotic regions
through the neck is even less than in the vacuum
(Schwarzschild-Kruskal-Szekeres) case. We investigate the anisotropic
generalisation of the wormhole topology in the Szekeres model. The function
E(r, p, q) describes the deviation from spherical symmetry if \partial_r E \neq
0, but this requires the mass to be increasing with radius, \partial_r M > 0,
i.e. non-zero density. We investigate the geometrical relations between the
mass dipole and the locii of apparent horizon and of shell-crossings. We
present the various conditions that ensure physically reasonable
quasi-spherical models, including a regular origin, regular maxima and minima
in the spatial sections, and the absence of shell-crossings. We show that
physically reasonable values of \partial_r E \neq 0 cannot compensate for the
effects of \partial_r M > 0 in any direction, so that communication through the
neck is still worse than the vacuum.
We also show that a handle topology cannot be created by identifying
hypersufaces in the two asymptotic regions on either side of a wormhole, unless
a surface layer is allowed at the junction. This impossibility includes the
Schwarzschild-Kruskal-Szekeres case.Comment: zip file with LaTeX text + 6 figures (.eps & .ps). 47 pages. Second
replacement corrects some minor errors and typos. (First replacement prints
better on US letter size paper.

### A Simple Family of Analytical Trumpet Slices of the Schwarzschild Spacetime

We describe a simple family of analytical coordinate systems for the
Schwarzschild spacetime. The coordinates penetrate the horizon smoothly and are
spatially isotropic. Spatial slices of constant coordinate time $t$ feature a
trumpet geometry with an asymptotically cylindrical end inside the horizon at a
prescribed areal radius $R_0$ (with $0<R_{0}\leq M$) that serves as the free
parameter for the family. The slices also have an asymptotically flat end at
spatial infinity. In the limit $R_{0}=0$ the spatial slices lose their trumpet
geometry and become flat -- in this limit, our coordinates reduce to
Painlev\'e-Gullstrand coordinates.Comment: 7 pages, 3 figure

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