41 research outputs found
Strong lensing in the Einstein-Straus solution
We analyse strong lensing in the Einstein-Straus solution with positive
cosmological constant. For concreteness we compare the theory to the light
deflection of the lensed quasar SDSS J1004+4112.Comment: 14 pages, 3 figures, 5 tables. To the memory of J\"urgen Ehlers v2
contains a note added during publication in GRG and less typo
Pressure as a Source of Gravity
The active mass density in Einstein's theory of gravitation in the analog of
Poisson's equation in a local inertial system is proportional to .
Here is the density of energy and its pressure for a perfect fluid.
By using exact solutions of Einstein's field equations in the static case we
study whether the pressure term contributes towards the mass
Time delay in the Einstein-Straus solution
The time delay of strong lensing is computed in the framework of the
Einstein-Straus solution. The theory is compared to the observational bound on
the time delay of the lens SDSS J1004+4112.Comment: 20 pages, 4 tables, 1 figur
Matching Spherical Dust Solutions to Construct Cosmological Models
Conditions for smooth cosmological models are set out and applied to
inhomogeneous spherically symmetric models constructed by matching together
different Lemaitre-Tolman-Bondi solutions to the
Einstein field equations. As an illustration the methods are applied to a
collapsing dust sphere in a curved background. This describes a region which
expands and then collapses to form a black hole in an
Einstein de Sitter background. We show that in all such models if there is no
vacuum region then the singularity must go on accreting matter for an infinite
LTB time.Comment: 13 pages, Revtex; to appear Gen. Rel. Gra
Interacting Constituents in Cosmology
Universe evolution, as described by Friedmann's equations, is determined by
source terms fixed by the choice of pressure energy-density equations
of state . The usual approach in Cosmology considers equations of
state accounting only for kinematic terms, ignoring the contribution from the
interactions between the particles constituting the source fluid. In this work
the importance of these neglected terms is emphasized. A systematic method,
based on the Statistical Mechanics of real fluids, is proposed to include them.
A toy-model is presented which shows how such interaction terms can engender
significant cosmological effects.Comment: 24 pages, 6 figures. It includes results presented in "Cosmic
Acceleration from Elementary Interactions" [arXiv:gr-qc/0512135]. Citations
added in v.
Singular shell embedded into a cosmological model
We generalize Israel's formalism to cover singular shells embedded in a
non-vacuum Universe. That is, we deduce the relativistic equation of motion for
a thin shell embedded in a Schwarzschild/Friedmann-Lemaitre-Robertson-Walker
spacetime. Also, we review the embedding of a Schwarzschild mass into a
cosmological model using "curvature" coordinates and give solutions with
(Sch/FLRW) and without the embedded mass (FLRW).Comment: 25 pages, 2 figure
Shear free solutions in General Relativity Theory
The Goldberg-Sachs theorem is an exact result on shear-free null geodesics in
a vacuum spacetime. It is compared and contrasted with an exact result for
pressure-free matter: shear-free flows cannot both expand and rotate. In both
cases, the shear-free condition restricts the way distant matter can influence
the local gravitational field. This leads to intriguing discontinuities in the
relation of the General Relativity solutions to Newtonian solutions in the
timelike case, and of the full theory to the linearised theory in the null
case.
It is a pleasure to dedicate this paper to Josh Goldberg.Comment: 17 pages, no figures. For GRG special issue in honor of Josh Goldber
Cosmological expansion and local systems: a Lema\^{i}tre-Tolman-Bondi model
We propose a Lema\^{i}tre-Tolman-Bondi system mimicking a two-body system to
address the problem of the cosmological expansion versus local dynamics. This
system is strongly bound but participates in the cosmic expansion and is
exactly comoving with the cosmic substratum
Theorems on shear-free perfect fluids with their Newtonian analogues
In this paper we provide fully covariant proofs of some theorems on
shear-free perfect fluids. In particular, we explicitly show that any
shear-free perfect fluid with the acceleration proportional to the vorticity
vector (including the simpler case of vanishing acceleration) must be either
non-expanding or non-rotating. We also show that these results are not
necessarily true in the Newtonian case, and present an explicit comparison of
shear-free dust in Newtonian and relativistic theories in order to see where
and why the differences appear.Comment: 23 pages, LaTeX. Submitted to GR
Quantization of the Closed Mini-Superspace Models as Bound States
Wheeler-DeWitt equation is applied to Friedmann Robertson Walker
metric with various types of matter. It is shown that if the Universe ends in
the matter dominated era (e.g., radiation or pressureless gas) with zero
cosmological constant, then the resulting Wheeler-DeWitt equation describes a
bound state problem. As solutions of a non-degenerate bound state system, the
eigen-wave functions are real (Hartle-Hawking) and the usual issue associated
with the ambiguity in the boundary conditions for the wave functions is
resolved. Furthermore, as a bound state problem, there exists a quantization
condition that relates the curvature of the three space with the energy density
of the Universe. Incorporating a cosmological constant in the early Universe
(inflation) is given as a natural explanation for the large quantum number
associated with our Universe, which resulted from the quantization condition.
It is also shown that if there is a cosmological constant in
our Universe that persists for all time, then the resulting Wheeler-DeWitt
equation describes a non-bound state system, regardless of the magnitude of the
cosmological constant. As a consequence, the wave functions are in general
complex (Vilenkin) and the initial conditions for wave functions are a free
parameters not determined by the formalism.Comment: 20