Threshold of Singularity Formation in the Semilinear Wave Equation

Solutions of the semilinear wave equation are found numerically in three spatial dimensions with no assumed symmetry using distributed adaptive mesh refinement. The threshold of singularity formation is studied for the two cases in which the exponent of the nonlinear term is either $p=5$ or $p=7$. Near the threshold of singularity formation, numerical solutions suggest an approach to self-similarity for the $p=7$ case and an approach to a scale evolving static solution for $p=5$.Comment: 6 pages, 7 figure

Orbital Dynamics of Binary Boson Star Systems

We extend our previous studies of head-on collisions of boson stars by considering orbiting binary boson stars. We concentrate on equal mass binaries and study the dynamical behavior of boson/boson and boson/antiboson pairs. We examine the gravitational wave output of these binaries and compare with other compact binaries. Such a comparison lets us probe the apparent simplicity observed in gravitational waves produced by black hole binary systems. In our system of interest however, there is an additional internal freedom which plays a significant role in the system's dynamics, namely the phase of each star. Our evolutions show rather simple behavior at early times, but large differences occur at late times for the various initial configurations.Comment: 10 pages, 14 figure

Critical Phenomena Inside Global Monopoles

The gravitational collapse of a triplet scalar field is examined assuming a hedgehog ansatz for the scalar field. Whereas the seminal work by Choptuik with a single, strictly spherically symmetric scalar field found a discretely self-similar (DSS) solution at criticality with echoing period $\Delta=3.44$, here a new DSS solution is found with period $\Delta=0.46$. This new critical solution is also observed in the presence of a symmetry breaking potential as well as within a global monopole. The triplet scalar field model contains Choptuik's original model in a certain region of parameter space, and hence his original DSS solution is also a solution. However, the choice of a hedgehog ansatz appears to exclude the original DSS.Comment: 5 pages, 5 figure

Singularity Formation in 2+1 Wave Maps

We present numerical evidence that singularities form in finite time during the evolution of 2+1 wave maps from spherically equivariant initial data of sufficient energy.Comment: 5 pages, 3 figure

Critical Collapse of the Massless Scalar Field in Axisymmetry

We present results from a numerical study of critical gravitational collapse of axisymmetric distributions of massless scalar field energy. We find threshold behavior that can be described by the spherically symmetric critical solution with axisymmetric perturbations. However, we see indications of a growing, non-spherical mode about the spherically symmetric critical solution. The effect of this instability is that the small asymmetry present in what would otherwise be a spherically symmetric self-similar solution grows. This growth continues until a bifurcation occurs and two distinct regions form on the axis, each resembling the spherically symmetric self-similar solution. The existence of a non-spherical unstable mode is in conflict with previous perturbative results, and we therefore discuss whether such a mode exists in the continuum limit, or whether we are instead seeing a marginally stable mode that is rendered unstable by numerical approximation.Comment: 11 pages, 8 figure

The Singularity Threshold of the Nonlinear Sigma Model Using 3D Adaptive Mesh Refinement

Numerical solutions to the nonlinear sigma model (NLSM), a wave map from 3+1 Minkowski space to S^3, are computed in three spatial dimensions (3D) using adaptive mesh refinement (AMR). For initial data with compact support the model is known to have two regimes, one in which regular initial data forms a singularity and another in which the energy is dispersed to infinity. The transition between these regimes has been shown in spherical symmetry to demonstrate threshold behavior similar to that between black hole formation and dispersal in gravitating theories. Here, I generalize the result by removing the assumption of spherical symmetry. The evolutions suggest that the spherically symmetric critical solution remains an intermediate attractor separating the two end states.Comment: 5 pages, 5 figures, 1 table; To be published in Phys. Rev. D.; Added discussion of initial data; Added figure and reference

Large Eddy Simulations of Magnetized Mergers of Neutron Stars with Neutrinos

Neutron star mergers are very violent events involving extreme physical processes: dynamic, strong-field gravity, large magnetic field, very hot, dense matter, and the copious production of neutrinos. Accurate modeling of such a system and its associated multi-messenger signals, such as gravitational waves, short gamma ray burst, and kilonova, requires the inclusion of all these processes, and is increasingly important in light of advancements in multi-messenger astronomy generally, and in gravitational wave astronomy in particular (such as the development of third-generation detectors). Several general relativistic codes have been incorporating some of these elements with different levels of realism. Here, we extend our code MHDuet, which can perform large eddy simulations of magnetohydrodynamics to help capture the magnetic field amplification during the merger, and to allow for realistic equations of state and neutrino cooling via a leakage scheme. We perform several tests involving isolated and binary neutron stars demonstrating the accuracy of the code.Comment: 20 pages, 11 figures (typos corrected

Head-on collisions of boson stars

We study head-on collisions of boson stars in three dimensions. We consider evolutions of two boson stars which may differ in their phase or have opposite frequencies but are otherwise identical. Our studies show that these phase differences result in different late time behavior and gravitational wave output

Black Hole Criticality in the Brans-Dicke Model

We study the collapse of a free scalar field in the Brans-Dicke model of gravity. At the critical point of black hole formation, the model admits two distinctive solutions dependent on the value of the coupling parameter. We find one solution to be discretely self-similar and the other to exhibit continuous self-similarity.Comment: 4 pages, REVTeX 3.0, 5 figures include