151 research outputs found
Perturbed Spherically Symmetric Dust Solution of the Field Equations in Observational Coordinates with Cosmological Data Functions
Using the framework for solving the spherically symmetric field equations in
observational coordinates given in Araujo and Stoeger (1999), their formulation
and solution in the perturbed FLRW sperically symmetric case with observational
data representing galaxy redshifts, number counts and observer area distances,
both as functions of redshift on our past light cone, are presented. The
importance of the central conditions, those which must hold on our world line
C, is emphasized. In detailing the solution for these perturbations, we discuss
the gauge problem and its resolution in this context, as well as how errors and
gaps in the data are propagated together with the genuine perturbations. This
will provide guidance for solving, and interpreting the solutions of the more
complicated general perturbation problem with observational data on our past
light cone.Comment: Latex 23 pages, no figures, submitted to Astrophysical Journa
Retarded coordinates based at a world line, and the motion of a small black hole in an external universe
In the first part of this article I present a system of retarded coordinates
based at an arbitrary world line of an arbitrary curved spacetime. The
retarded-time coordinate labels forward light cones that are centered on the
world line, the radial coordinate is an affine parameter on the null generators
of these light cones, and the angular coordinates are constant on each of these
generators. The spacetime metric in the retarded coordinates is displayed as an
expansion in powers of the radial coordinate and expressed in terms of the
world line's acceleration vector and the spacetime's Riemann tensor evaluated
at the world line. The formalism is illustrated in two examples, the first
involving a comoving world line of a spatially-flat cosmology, the other
featuring an observer in circular motion in the Schwarzschild spacetime. The
main application of the formalism is presented in the second part of the
article, in which I consider the motion of a small black hole in an empty
external universe. I use the retarded coordinates to construct the metric of
the small black hole perturbed by the tidal field of the external universe, and
the metric of the external universe perturbed by the presence of the black
hole. Matching these metrics produces the MiSaTaQuWa equations of motion for
the small black hole.Comment: 20 pages, revtex4, 2 figure
Obtaining the spacetime metric from cosmological observations
Recent galaxy redshift surveys have brought in a large amount of accurate
cosmological data out to redshift 0.3, and future surveys are expected to
achieve a high degree of completeness out to a redshift exceeding 1.
Consequently, a numerical programme for determining the metric of the universe
from observational data will soon become practical; and thereby realise the
ultimate application of Einstein's equations. Apart from detailing the cosmic
geometry, this would allow us to verify and quantify homogeneity, rather than
assuming it, as has been necessary up to now, and to do that on a metric level,
and not merely at the mass distribution level. This paper is the beginning of a
project aimed at such a numerical implementation. The primary observational
data from our past light cone consists of galaxy redshifts, apparent
luminosities, angular diameters and number densities, together with source
evolution functions, absolute luminosities, true diameters and masses of
sources. Here we start with the simplest case, that of spherical symmetry and a
dust equation of state, and execute an algorithm that determines the unknown
metric functions from this data. We discuss the challenges of turning the
theoretical algorithm into a workable numerical procedure, particularly
addressing the origin and the maximum in the area distance. Our numerical
method is tested with several artificial data sets for homogeneous and
inhomogeneous models, successfully reproducing the original models. This
demonstrates the basic viability of such a scheme. Although current surveys
don't have sufficient completeness or accuracy, we expect this situation to
change in the near future, and in the meantime there are many refinements and
generalisations to be added.Comment: 26 pages, 10 figures. Minor changes to match the published versio
On perfect fluid models in non-comoving observational spherical coordinates
We use null spherical (observational) coordinates to describe a class of
inhomogeneous cosmological models. The proposed cosmological construction is
based on the observer past null cone. A known difficulty in using inhomogeneous
models is that the null geodesic equation is not integrable in general. Our
choice of null coordinates solves the radial ingoing null geodesic by
construction. Furthermore, we use an approach where the velocity field is
uniquely calculated from the metric rather than put in by hand. Conveniently,
this allows us to explore models in a non-comoving frame of reference. In this
frame, we find that the velocity field has shear, acceleration and expansion
rate in general. We show that a comoving frame is not compatible with expanding
perfect fluid models in the coordinates proposed and dust models are simply not
possible. We describe the models in a non-comoving frame. We use the dust
models in a non-comoving frame to outline a fitting procedure.Comment: 8 pages, 1 figure. To appear in Phys.Rev.
Almost-homogeneity of the universe in higher-order gravity
In the gravity theory, we show that if freely propagating
massless particles have an almost isotropic distribution, then the spacetime is
almost Friedmann-Robertson-Walker (FRW). This extends the result proved
recently in general relativity (), which is applicable to the
microwave background after photon decoupling. The higher-order result is in
principle applicable to a massless species that decouples in the early
universe, such as a relic graviton background. Any future observations that
show small anisotropies in such a background would imply that the geometry of
the early universe were almost FRW.Comment: 14 pages LaTeX, no figures; to appear in General Relativity and
Gravitatio
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