69 research outputs found
More examples of structure formation in the Lemaitre-Tolman model
In continuing our earlier research, we find the formulae needed to determine
the arbitrary functions in the Lemaitre-Tolman model when the evolution
proceeds from a given initial velocity distribution to a final state that is
determined either by a density distribution or by a velocity distribution. In
each case the initial and final distributions uniquely determine the L-T model
that evolves between them, and the sign of the energy-function is determined by
a simple inequality. We also show how the final density profile can be more
accurately fitted to observational data than was done in our previous paper. We
work out new numerical examples of the evolution: the creation of a galaxy
cluster out of different velocity distributions, reflecting the current data on
temperature anisotropies of CMB, the creation of the same out of different
density distributions, and the creation of a void. The void in its present
state is surrounded by a nonsingular wall of high density.Comment: LaTeX 2e with eps figures. 30 pages, 11 figures, 30 figure files.
Revision matches published versio
Comment on `Smooth and Discontinuous Signature Type Change in General Relativity'
Kossowski and Kriele derived boundary conditions on the metric at a surface
of signature change. We point out that their derivation is based not only on
certain smoothness assumptions but also on a postulated form of the Einstein
field equations. Since there is no canonical form of the field equations at a
change of signature, their conclusions are not inescapable. We show here that a
weaker formulation is possible, in which less restrictive smoothness
assumptions are made, and (a slightly different form of) the Einstein field
equations are satisfied. In particular, in this formulation it is possible to
have a bounded energy-momentum tensor at a change of signature without
satisfying their condition that the extrinsic curvature vanish.Comment: Plain TeX, 6 pages; Comment on Kossowski and Kriele: Class. Quantum
Grav. 10, 2363 (1993); Reply by Kriele: Gen. Rel. Grav. 28, 1409-1413 (1996
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.
Clumps into Voids
We consider a spherically symmetric distribution of dust and show that it is
possible, under general physically reasonable conditions, for an overdensity to
evolve to an underdensity (and vice versa). We find the conditions under which
this occurs and illustrate it on a class of regular Lemaitre-Tolman-Bondi
solutions. The existence of this phenomenon, if verified, would have the result
that the topology of density contours, assumed fixed in standard structure
formation theories, would have to change and that luminous matter would not
trace the dark matter distribution so well.Comment: LaTeX, 17 pages, 4 figures. Submitted to GRG 20/4/200
Note on Signature Change and Colombeau Theory
Recent work alludes to various `controversies' associated with signature
change in general relativity. As we have argued previously, these are in fact
disagreements about the (often unstated) assumptions underlying various
possible approaches. The choice between approaches remains open.Comment: REVTex, 3 pages; to appear in GR
Formation of a galaxy with a central black hole in the Lemaitre-Tolman model
We construct two models of the formation a galaxy with a central black hole,
starting from a small initial fluctuation at recombination. This is an
application of previously developed methods to find a Lemaitre-Tolman model
that evolves from a given initial density or velocity profile to a given final
density profile. We show that the black hole itself could be either a collapsed
object, or a non-vacuum generalisation of a full Schwarzschild-Kruskal-Szekeres
wormhole. Particular attention is paid to the black hole's apparent and event
horizons.Comment: REVTeX, 22 pages including 11 figures (25 figure files). Replacement
has minor changes in response to the referee, and editorial corrections. To
appear in PR
Reply Comment: Comparison of Approaches to Classical Signature Change
We contrast the two approaches to ``classical" signature change used by
Hayward with the one used by us (Hellaby and Dray). There is (as yet) no
rigorous derivation of appropriate distributional field equations. Hayward's
distributional approach is based on a postulated modified form of the field
equations. We make an alternative postulate. We point out an important
difference between two possible philosophies of signature change --- ours is
strictly classical, while Hayward's Lagrangian approach adopts what amounts to
an imaginary proper ``time" on one side of the signature change, as is
explicitly done in quantum cosmology. We also explain why we chose to use the
Darmois-Israel type junction conditions, rather than the Lichnerowicz type
junction conditions favoured by Hayward. We show that the difference in results
is entirely explained by the difference in philosophy (imaginary versus real
Euclidean ``time"), and not by the difference in approach to junction
conditions (Lichnerowicz with specific coordinates versus Darmois with general
coordinates).Comment: 10 pages, latex, no figures. Replying to - "Comment on `Failure of
Standard Conservation Laws at a Classical Change of Signature'", S.A.
Hayward, Phys. Rev. D52, 7331-7332 (1995) (gr-qc/9606045
The Hubble Diagram of Type Ia Supernovae in Non-Uniform Pressure Universes
We use the redshift-magnitude relation, as derived by D\c{a}browski (1995),
for the two exact non-uniform pressure spherically symmetric Stephani universes
with the observer positioned at the center of symmetry, to test the agreement
of these models with recent observations of high redshift type Ia supernovae
(SNIa), as reported in Perlmutter et al. (1997). By a particular choice of
model parameters, we show that these models give an excellent fit to the
observed redshifts and (corrected) B band apparent magnitudes of the SNIa data,
but for an age of the Universe which is typically about two Gyr greater than in
the corresponding Friedmann model.
Based on a value of and assuming , the P97 data
implies a Friedmann age of at most 13 Gyr and in fact a best-fit (for ) age of only 10 Gyr. Our Stephani models, on the other hand, can give a
good fit to the P97 data with an age of up to 15 Gyr and could, therefore,
significantly alleviate the conflict between recent cosmological and
astrophysical age predictions. The choice of model parameters is quite robust:
one requires only that the non-uniform pressure parameter, , in one of the
models is negative and satisfies |a| \lte 3 km s Mpc. By
allowing slightly larger, negative, values of one may `fine tune' the model
to give an even better fit to the P97 data.Comment: 36 pages, 2 tables, 6 figures, AAS Latex 4.0, vastly revised version,
new title and abstract, to appear in Ap
Nondifferentiable Dynamic: Two Examples
Some nondifferentiable quantities (for example, the metric signature) can be
the independent physical degrees of freedom. It is supposed that in quantum
gravity these degrees of freedom can fluctuate. Two examples of such quantum
fluctuation are considered: a quantum interchange of the sign of two components
of the 5D metric and a quantum fluctuation between Euclidean and Lorentzian
metrics. The first case leads to a spin-like structure on the throat of
composite wormhole and to a possible inner structure of the string. The second
case leads to a quantum birth of the non-singular Euclidean Universe with
frozen dimension. The probability for such quantum fluctuations is
connected with an algorithmical complexity of the Einstein equations.Comment: essential changes: the initial equations in section III are changed,
as the consequence the obtained solution describes the quantum birth of the
nonsingular Universe with the matter (electromagnetic field=nondiagonal
components of the MD metric
Casimir stress on parallel plates in de Sitter space with signature change
The Casimir stress on two parallel plates in a de Sitter background
corresponding to different metric signatures and cosmological constants is
calculated for massless scalar fields satisfying Robin boundary conditions on
the plates. Our calculation shows that for the parallel plates with false
vacuum between and true vacuum outside, the total Casimir pressure leads to an
attraction of the plates at very early universe.Comment: 9 pages, no figures, accepted for publication in IJMP
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