2,885 research outputs found
Choptuik scaling in null coordinates
A numerical simulation is performed of the gravitational collapse of a
spherically symmetric scalar field. The algorithm uses the null initial value
formulation of the Einstein-scalar equations, but does {\it not} use adaptive
mesh refinement. A study is made of the critical phenomena found by Choptuik in
this system. In particular it is verified that the critical solution exhibits
periodic self-similarity. This work thus provides a simple algorithm that gives
verification of the Choptuik results.Comment: latex (revtex), 6 figures included in the fil
The spherically symmetric collapse of a massless scalar field
We report on a numerical study of the spherically symmetric collapse of a
self-gravitating massless scalar field. Earlier results of Choptuik(1992, 1994)
are confirmed. The field either disperses to infinity or collapses to a black
hole, depending on the strength of the initial data. For evolutions where the
strength is close to but below the strength required to form a black hole, we
argue that there will be a region close to the axis where the scalar curvature
and field energy density can reach arbitrarily large levels, and which is
visible to distant observersComment: 23 pages, 16 figures, uuencoded gzipped postscript This version omits
2 pages of figures. This file, the two pages of figures and the complete
paper are available at ftp://ftp.damtp.cam.ac.uk/pub/gr/rsh100
A Striking Confluence Between Theory and Observations of High-Mass X-ray Binary Pulsars
We analyse the most powerful X-ray outbursts from neutron stars in ten
Magellanic high-mass X-ray binaries and three pulsating ultraluminous X-ray
sources. Most of the outbursts rise to which is about the level of
the Eddington luminosity, while the rest and more powerful outbursts also
appear to recognize that limit when their emissions are assumed to be
anisotropic and beamed toward our direction. We use the measurements of pulsar
spin periods and their derivatives to calculate the X-ray
luminosities in their faintest accreting ("propeller") states. In four
cases with unknown , we use the lowest observed X-ray luminosities,
which only adds to the heterogeneity of the sample. Then we calculate the
ratios and we obtain an outstanding confluence of theory and
observations from which we conclude that work done on both fronts is accurate
and the results are trustworthy: sources known to reside on the lowest
Magellanic propeller line are all located on/near that line, whereas other
sources jump higher and reach higher-lying propeller lines. These jumps can be
interpreted in only one way, higher-lying pulsars have stronger surface
magnetic fields in agreement with empirical results in which and
values were not used.Comment: Added LMC X-4 and commented on the cyclotron absorption line of SMC
X-2. 4 pages, 1 figure, 2 tables, submitted to MNRAS
Self-gravitating Klein-Gordon fields in asymptotically Anti-de-Sitter spacetimes
We initiate the study of the spherically symmetric Einstein-Klein-Gordon
system in the presence of a negative cosmological constant, a model appearing
frequently in the context of high-energy physics. Due to the lack of global
hyperbolicity of the solutions, the natural formulation of dynamics is that of
an initial boundary value problem, with boundary conditions imposed at null
infinity. We prove a local well-posedness statement for this system, with the
time of existence of the solutions depending only on an invariant H^2-type norm
measuring the size of the Klein-Gordon field on the initial data. The proof
requires the introduction of a renormalized system of equations and relies
crucially on r-weighted estimates for the wave equation on asymptotically AdS
spacetimes. The results provide the basis for our companion paper establishing
the global asymptotic stability of Schwarzschild-Anti-de-Sitter within this
system.Comment: 50 pages, v2: minor changes, to appear in Annales Henri Poincar\'
Exact solution for scalar field collapse
We give an exact spherically symmetric solution for the Einstein-scalar field
system. The solution may be interpreted as an inhomogeneous dynamical scalar
field cosmology. The spacetime has a timelike conformal Killing vector field
and is asymptotically conformally flat. It also has black or white hole-like
regions containing trapped surfaces. We describe the properties of the apparent
horizon and comment on the relevance of the solution to the recently discovered
critical behaviour in scalar field collapse.Comment: 10 pages(Latex) (2 figures available upon request), Alberta-Thy-4-9
The formation of black holes in spherically symmetric gravitational collapse
We consider the spherically symmetric, asymptotically flat Einstein-Vlasov
system. We find explicit conditions on the initial data, with ADM mass M, such
that the resulting spacetime has the following properties: there is a family of
radially outgoing null geodesics where the area radius r along each geodesic is
bounded by 2M, the timelike lines are incomplete, and for r>2M
the metric converges asymptotically to the Schwarzschild metric with mass M.
The initial data that we construct guarantee the formation of a black hole in
the evolution. We also give examples of such initial data with the additional
property that the solutions exist for all and all Schwarzschild time,
i.e., we obtain global existence in Schwarzschild coordinates in situations
where the initial data are not small. Some of our results are also established
for the Einstein equations coupled to a general matter model characterized by
conditions on the matter quantities.Comment: 36 pages. A corollary on global existence in Schwarzschild
coordinates for data which are not small is added together with minor
modification
Phase-Transition Theory of Instabilities. II. Fourth-Harmonic Bifurcations and Lambda-Transitions
We use a free-energy minimization approach to describe the secular and
dynamical instabilities as well as the bifurcations along equilibrium sequences
of rotating, self-gravitating fluid systems. Our approach is fully nonlinear
and stems from the Ginzburg-Landau theory of phase transitions. In this paper,
we examine fourth-harmonic axisymmetric disturbances in Maclaurin spheroids and
fourth-harmonic nonaxisymmetric disturbances in Jacobi ellipsoids. These two
cases are very similar in the framework of phase transitions. Irrespective of
whether a nonlinear first-order phase transition occurs between the critical
point and the higher turning point or an apparent second-order phase transition
occurs beyond the higher turning point, the result is fission (i.e.
``spontaneous breaking'' of the topology) of the original object on a secular
time scale: the Maclaurin spheroid becomes a uniformly rotating axisymmetric
torus and the Jacobi ellipsoid becomes a binary. The presence of viscosity is
crucial since angular momentum needs to be redistributed for uniform rotation
to be maintained. The phase transitions of the dynamical systems are briefly
discussed in relation to previous numerical simulations of the formation and
evolution of protostellar systems.Comment: 34 pages, postscript, compressed,uuencoded. 7 figures available in
postscript, compressed form by anonymous ftp from asta.pa.uky.edu (cd
/shlosman/paper2 mget *.ps.Z). To appear in Ap
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