We examine the gravitational collapse of sphaleron type configurations in Einstein--Yang--Mills--Higgs theory. Working in spherical symmetry, we investigate the critical behavior in this model. We provide evidence that for various initial configurations, there can be three different critical transitions between possible endstates with different critical solutions sitting on the threshold between these outcomes. In addition, we show that within the dispersive and black hole regimes, there are new possible endstates, namely a stable, regular sphaleron and a stable, hairy black hole.

R. Steven Millward Eric W. Hirschmann

We consider the collapse of a global "Hopf" texture and examine the conjecture, disputed in the literature, that monopole-antimonopole pairs can be formed in the process. We show that such monopole-antimonopole pairs can indeed be nucleated in the course of texture collapse given appropriate initial conditions. The subsequent dynamics include the recombination and annihilation of the pair in a burst of outgoing scalar radiation.

Eric W. Hirschmann Steven L. Liebling

We consider the orbits of particles with spin in the Schwarzschild spacetime. Using the Papapetrou-Dixon equations of motion for spinning particles, we solve for the orbits and focus on those that exhibit chaos using both Poincar\'e maps and Lyapunov exponents. In particular, we develop a method for comparing the Lyapunov exponents of chaotic orbits. We find chaotic orbits for smaller spin values than previously thought and with spins that could be realized astrophysically.

Chris Verhaaren Eric W. Hirschmann

A new algorithm for solving the general relativistic MHD equations is described in this paper. We design our scheme to incorporate black hole excision with smooth boundaries, and to simplify solving the combined Einstein and MHD equations with AMR. The fluid equations are solved using a finite difference Convex ENO method. Excision is implemented using overlapping grids. Elliptic and hyperbolic divergence cleaning techniques allow for maximum flexibility in choosing coordinate systems, and we compare both methods for a standard problem. Numerical results of standard test problems are presented in two-dimensional flat space using excision, overlapping grids, and elliptic and hyperbolic divergence cleaning.

David Neilsen Eric W Hirschmann R Steven Millward

This paper studies gravitational collapse of a complex scalar field at the threshold for black hole formation, assuming that the collapse is spherically symmetric and continuously self-similar. A new solution of the coupled Einstein-scalar field equations is derived, after a small amount of numerical work with ordinary differential equations. The universal scaling and echoing behavior discovered by Choptuik in spherically symmetrical gravitational collapse appear in a somewhat different form. Properties of the endstate of the collapse are derived: The collapse leaves behind an irregular outgoing pulse of scalar radiation, with exactly flat spacetime within it.

Eric W. Hirschmann Douglas M. Eardley

We study gravitational collapse of the axion/dilaton field in classical low energy string theory, at the threshold for black hole formation. A new critical solution is derived that is spherically symmetric and continuously self-similar. The universal scaling and echoing behavior discovered by Choptuik in gravitational collapse appear in a somewhat different form. In particular, echoing takes the form of SL(2,R) rotations (cf. S-duality). The collapse leaves behind an outgoing pulse of axion/dilaton radiation, with nearly but not exactly flat spacetime within it.

Douglas M. Eardley Eric W. Hirschmann James H. Horne

This paper continues a study on Choptuik scaling in gravitational collapse of a complex scalar field at the threshold for black hole formation. We perform a linear perturbation analysis of the previously derived complex critical solution, and calculate the critical exponent for black hole mass, $\gamma \approx 0.387106$. We also show that this critical solution is unstable via a growing oscillatory mode.

Eric W. Hirschmann Douglas M. Eardley

We consider solutions to the nonlinear sigma model (wave maps) with target space S^3 and base space 3+1 Minkowski space, and we find critical behavior separating singular solutions from nonsingular solutions. For families of solutions with localized spatial support a self-similar solution is found at the boundary. For other families, we find that a static solution appears to sit at the boundary. This behavior is compared to the black hole critical phenomena found by Choptuik.

Steven L. Liebling Eric W. Hirschmann James Isenberg

We model two mergers of orbiting binary neutron stars, the first forming a black hole and the second a differentially rotating neutron star. We extract gravitational waveforms in the wave zone. Comparisons to a post-Newtonian analysis allow us to compute the orbital kinematics, including trajectories and orbital eccentricities. We verify our code by evolving single stars and extracting radial perturbative modes, which compare very well to results from perturbation theory. The Einstein equations are solved in a first order reduction of the generalized harmonic formulation, and the fluid equations are solved using a modified convex essentially non-oscillatory method. All calculations are done in three spatial dimensions without symmetry assumptions. We use the \had computational infrastructure for distributed adaptive mesh refinement.

Matthew Anderson Eric W. Hirschmann Luis Lehner Steven L. Liebling Patrick M. Motl David Neilsen Carlos Palenzuela Joel E. Tohline

We investigate the influence of magnetic fields upon the dynamics of and resulting gravitational waves from a binary neutron star merger in full general relativity coupled to ideal magnetohydrodynamics (MHD). We consider two merger scenarios, one where the stars begin with initially aligned poloidal magnetic fields and one with no magnetic field. Both mergers result in a strongly differentially rotating object. In comparison to the non-magnetized scenario, the aligned magnetic fields delay the final merger of the two stars. During and after merger we observe phenomena driven by the magnetic field, including Kelvin-Helmholtz instabilities in shear layers, winding of the field lines, and transition from poloidal to toroidal fields. These effects not only produce electromagnetic radiation, but also can have a strong influence on the gravitational waves. Thus, there are promising prospects for studying such systems with both types of waves.

Matthew Anderson Eric W. Hirschmann Luis Lehner Steven L. Liebling Patrick M. Motl David Neilsen Carlos Palenzuela Joel E. Tohline