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: ) 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
Explicit Global Coordinates for Schwarzschild and Reissner-Nordstroem
We construct coordinate systems that cover all of the Reissner-Nordstroem
solution with m>|q| and m=|q|, respectively. This is possible by means of
elementary analytical functions. The limit of vanishing charge q provides an
alternative to Kruskal which, to our mind, is more explicit and simpler. The
main tool for finding these global charts is the description of highly
symmetrical metrics by two-dimensional actions. Careful gauge fixing yields
global representatives of the two-dimensional theory that can be rewritten
easily as the corresponding four-dimensional line elements.Comment: 12 pages, 3 Postscript figures, sign error in Eq. (37) and below
corrected, references and Note added; to appear in Class. Quantum Gra
On the global visibility of singularity in quasi-spherical collapse
We analyze here the issue of local versus the global visibility of a
singularity that forms in gravitational collapse of a dust cloud, which has
important implications for the weak and strong versions of the cosmic
censorship hypothesis. We find conditions as to when a singularity will be only
locally naked, rather than being globally visible, thus preseving the weak
censorship hypothesis. The conditions for formation of a black hole or naked
singularity in the Szekeres quasi-spherical collapse models are worked out. The
causal behaviour of the singularity curve is studied by examining the outgoing
radial null geodesics, and the final outcome of collapse is related to the
nature of the regular initial data specified on an initial hypersurface from
which the collapse evolves. An interesting feature that emerges is the
singularity in Szekeres spacetimes can be ``directionally naked''.Comment: Latex file, 32 pages, 12 postscript figures. To appear in the Journal
of General Relativity and Gravitatio
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 feature a
trumpet geometry with an asymptotically cylindrical end inside the horizon at a
prescribed areal radius (with ) that serves as the free
parameter for the family. The slices also have an asymptotically flat end at
spatial infinity. In the limit 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
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
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