840 research outputs found
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
Integer Partitions and Exclusion Statistics
We provide a combinatorial description of exclusion statistics in terms of
minimal difference partitions. We compute the probability distribution of
the number of parts in a random minimal partition. It is shown that the
bosonic point is a repulsive fixed point for which the limiting
distribution has a Gumbel form. For all positive the distribution is shown
to be Gaussian.Comment: 16 pages, 4 .eps figures include
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
Some notes on the Kruskal - Szekeres completion
The Kruskal - Szekeres (KS) completion of the Schwarzschild spacetime is open
to Synge's methodological criticism that the KS procedure generates "good"
coordinates from "bad". This is addressed here in two ways: First I generate
the KS coordinates from Israel coordinates, which are also "good", and then I
generate the KS coordinates directly from a streamlined integration of the
Einstein equations.Comment: One typo correcte
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
A Radiation Scalar for Numerical Relativity
This letter describes a scalar curvature invariant for general relativity
with a certain, distinctive feature. While many such invariants exist, this one
vanishes in regions of space-time which can be said unambiguously to contain no
gravitational radiation. In more general regions which incontrovertibly support
non-trivial radiation fields, it can be used to extract local,
coordinate-independent information partially characterizing that radiation.
While a clear, physical interpretation is possible only in such radiation
zones, a simple algorithm can be given to extend the definition smoothly to
generic regions of space-time.Comment: 4 pages, 1 EPS figur
No-Go Theorem in Spacetimes with Two Commuting Spacelike Killing Vectors
Four-dimensional Riemannian spacetimes with two commuting spacelike Killing
vectors are studied in Einstein's theory of gravity, and found that no outer
apparent horizons exist, provided that the dominant energy condition holds.Comment: latex, 1 figure, version published in Gen. Relativ. Grav., 37,
1919-1926 (2005
Collisions of Einstein-Conformal Scalar Waves
A large class of solutions of the Einstein-conformal scalar equations in
D=2+1 and D=3+1 is identified. They describe the collisions of asymptotic
conformal scalar waves and are generated from Einstein-minimally coupled scalar
spacetimes via a (generalized) Bekenstein transformation. Particular emphasis
is given to the study of the global properties and the singularity structure of
the obtained solutions. It is shown, that in the case of the absence of pure
gravitational radiation in the initial data, the formation of the final
singularity is not only generic, but is even inevitable.Comment: 17 pages, LaTe
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