3,546 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

### Self-Similar Scalar Field Collapse: Naked Singularities and Critical Behaviour

Homothetic scalar field collapse is considered in this article. By making a
suitable choice of variables the equations are reduced to an autonomous system.
Then using a combination of numerical and analytic techniques it is shown that
there are two classes of solutions. The first consists of solutions with a
non-singular origin in which the scalar field collapses and disperses again.
There is a singularity at one point of these solutions, however it is not
visible to observers at finite radius. The second class of solutions includes
both black holes and naked singularities with a critical evolution (which is
neither) interpolating between these two extremes. The properties of these
solutions are discussed in detail. The paper also contains some speculation
about the significance of self-similarity in recent numerical studies.Comment: 27 pages including 5 encapsulated postcript figures in separate
compressed file, report NCL94-TP1

### Decay of the Maxwell field on the Schwarzschild manifold

We study solutions of the decoupled Maxwell equations in the exterior region
of a Schwarzschild black hole. In stationary regions, where the Schwarzschild
coordinate $r$ ranges over $2M < r_1 < r < r_2$, we obtain a decay rate of
$t^{-1}$ for all components of the Maxwell field. We use vector field methods
and do not require a spherical harmonic decomposition.
In outgoing regions, where the Regge-Wheeler tortoise coordinate is large,
$r_*>\epsilon t$, we obtain decay for the null components with rates of
$|\phi_+| \sim |\alpha| < C r^{-5/2}$, $|\phi_0| \sim |\rho| + |\sigma| < C
r^{-2} |t-r_*|^{-1/2}$, and $|\phi_{-1}| \sim |\underline{\alpha}| < C r^{-1}
|t-r_*|^{-1}$. Along the event horizon and in ingoing regions, where $r_*<0$,
and when $t+r_*1$, all components (normalized with respect to an ingoing null
basis) decay at a rate of C \uout^{-1} with \uout=t+r_* in the exterior
region.Comment: 37 pages, 5 figure

### Spherically symmetric perfect fluid in area-radial coordinates

We study the spherically symmetric collapse of a perfect fluid using
area-radial coordinates. We show that analytic mass functions describe a static
regular centre in these coordinates. In this case, a central singularity can
not be realized without an infinite discontinuity in the central density. We
construct mass functions involving fluid dynamics at the centre and investigate
the relationship between those and the nature of the singularities.Comment: Accepted by CQG. LaTex file, 14 pages, no figure

### 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 $r=c\in [0,2M]$ 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 $r\geq 0$ 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

### 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\'

### 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

### 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

### 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 $L_{max}$ 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 $P_S$ and their derivatives $\dot{P_S}$ to calculate the X-ray
luminosities $L_p$ in their faintest accreting ("propeller") states. In four
cases with unknown $\dot{P_S}$, we use the lowest observed X-ray luminosities,
which only adds to the heterogeneity of the sample. Then we calculate the
ratios $L_p/L_{max}$ 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 $\dot{P_S}$ and
$L_p$ 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

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