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 $L_{max}$ 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

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

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 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

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