496 research outputs found
Structure formation in the Lemaitre-Tolman model
Structure formation within the Lemaitre-Tolman model is investigated in a
general manner. We seek models such that the initial density perturbation
within a homogeneous background has a smaller mass than the structure into
which it will develop, and the perturbation then accretes more mass during
evolution. This is a generalisation of the approach taken by Bonnor in 1956. It
is proved that any two spherically symmetric density profiles specified on any
two constant time slices can be joined by a Lemaitre-Tolman evolution, and
exact implicit formulae for the arbitrary functions that determine the
resulting L-T model are obtained. Examples of the process are investigated
numerically.Comment: LaTeX 2e plus 14 .eps & .ps figure files. 33 pages including figures.
Minor revisions of text and data make it more precise and consistent.
Currently scheduled for Phys Rev D vol 64, December 15 issu
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.
The gravitational wave rocket
Einstein's equations admit solutions corresponding to photon rockets. In
these a massive particle recoils because of the anisotropic emission of
photons. In this paper we ask whether rocket motion can be powered only by the
emission of gravitational waves. We use the double series approximation method
and show that this is possible. A loss of mass and gain in momentum arise in
the second approximation because of the emission of quadrupole and octupole
waves.Comment: 10 pages LaTe
Detection of the gravitomagnetic clock effect
The essence of the gravitomagnetic clock effect is properly defined showing
that its origin is in the topology of world lines with closed space
projections. It is shown that, in weak field approximation and for a
spherically symmetric central body, the loss of synchrony between two clocks
counter-rotating along a circular geodesic is proportional to the angular
momentum of the source of the gravitational field. Numerical estimates are
presented for objects within the solar system. The less unfavorable situation
is found around Jupiter.Comment: 14 pages; Latex. To be published on Classical and Quantum Gravit
Evolution of the density contrast in inhomogeneous dust models
With the help of families of density contrast indicators, we study the
tendency of gravitational systems to become increasingly lumpy with time.
Depending upon their domain of definition, these indicators could be local or
global. We make a comparative study of these indicators in the context of
inhomogeneous cosmological models of Lemaitre--Tolman and Szekeres. In
particular, we look at the temporal asymptotic behaviour of these indicators
and ask under what conditions, and for which class of models, they evolve
monotonically in time. We find that for the case of ever-expanding models,
there is a larger class of indicators that grow monotonically with time,
whereas the corresponding class for the recollapsing models is more restricted.
Nevertheless, in the absence of decaying modes, indicators exist which grow
monotonically with time for both ever-expanding and recollapsing models
simultaneously. On the other hand, no such indicators may found which grow
monotonically if the decaying modes are allowed to exist. We also find the
conditions for these indicators to be non-divergent at the initial singularity
in both models. Our results can be of potential relevance for understanding
structure formation in inhomogeneous settings and in debates regarding
gravitational entropy and arrow of time. In particular, the spatial dependence
of turning points in inhomogeneous cosmologies may result in multiple density
contrast arrows in recollapsing models over certain epochs. We also find that
different notions of asymptotic homogenisation may be deduced, depending upon
the density contrast indicators used.Comment: 22 pages, 1 figure. To be published in Classical and Quantum Gravit
Classical gravitational spin-spin interaction
I obtain an exact, axially symmetric, stationary solution of Einstein's
equations for two massless spinning particles. The term representing the
spin-spin interaction agrees with recently published approximate work. The
spin-spin force appears to be proportional to the inverse fourth power of the
coordinate distance between the particles.Comment: six pages, no figures, journal ref:accepted for Classical and Quantum
Gravit
Levi-Civita Solutions Coupled with Electromagnetic Fields
The local and global properties of the Levi-Civita (LC) solutions coupled
with an electromagnetic field are studied and some limits to the vacuum LC
solutions are given. By doing such limits, the physical and geometrical
interpretations of the free parameters involved in the solutions are made
clear. Sources for both the LC vacuum solutions and the LC solutions coupled
with an electromagnetic field are studied, and in particular it is found that
all the LC vacuum solutions with can be produced by
cylindrically symmetric thin shells that satisfy all the energy conditions,
weak, dominant, and strong. When the electromagnetic field is present, the
situation changes dramatically. In the case of a purely magnetic field, all the
solutions with or can be
produced by physically acceptable cylindrical thin shells, while in the case of
a purely electric field, no such shells are found for any value of .Comment: Typed in Revtex, including two figure
Naked Singularities in the Charged Vaidya-deSitter Spacetime
We study the occurrence of naked singularities in the spherically symmetric
collapse of a charged null fluid in an expanding deSitter background - a piece
of charged Vaidya-deSitter spacetime. The necessary conditions for the
formation of a naked singularity are found. The results for the uncharged
solutions can be recovered from our analysis.Comment: 8 pages, latex, no figure
Magnetically Controlled Spasmodic Accretion During Star Formation. II. Results
The problem of the late accretion phase of the evolution of an axisymmetric,
isothermal magnetic disk surrounding a forming star has been formulated in a
companion paper. The "central sink approximation" is used to circumvent the
problem of describing the evolution inside the opaque central region for
densities greater than 10^11 cm^-3 and radii smaller than a few AUs. Only the
electrons are assumed to be attached to the magnetic field lines, and the
effects of both negatively and positively charged grains are accounted for.
After a mass of 0.1 solar mass accumulates in the central cell (forming star),
a series of magnetically driven outflows and associated outward propagating
shocks form in a quasi-periodic fashion. As a result, mass accretion onto the
protostar occurs in magnetically controlled bursts. We refer to this process as
spasmodic accretion. The shocks propagate outward with supermagnetosonic
speeds. The period of dissipation and revival of the outflow decreases in time,
as the mass accumulated in the central sink increases. We evaluate the
contribution of ambipolar diffusion to the resolution of the magnetic flux
problem of star formation during the accretion phase, and we find it to be very
significant although not sufficient to resolve the entire problem yet. Ohmic
dissipation is completely negligible in the disk during this phase of the
evolution. The protostellar disk is found to be stable against interchange-like
instabilities, despite the fact that the mass-to-flux ratio has temporary local
maxima.Comment: Astrophysical Journal, in press. 29 pages, 13 figure
Colliding axisymmetric pp-waves
An exact solution is found describing the collision of axisymmetric pp-waves
with M=0. They are impulsive in character and their coordinate singularities
become point curvature singularities at the boundaries of the interaction
region. The solution is conformally flat. Concrete examples are given,
involving an ultrarelativistic black hole against a burst of pure radiation or
two colliding beam- like waves.Comment: 6 pages, REVTeX, some misprints are correcte
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