Session R10: Topics in Numerical Relativity

Magnetic field effects on gravitational waves from binary neutron stars

Observational evidence indicates that a fair number of neutron star binaries and neutron star-black hole binaries have a sizable magnetic field which can be responsible for powering pulsars and colimating jets. Magnetic field effects additionally can have a strong influence on the dynamics of the fluid by redistributing angular momentum through different mechanisms (magnetic winding and braking, magneto-rotational instabilities) depending on the strength of the magnetic field and the typical time scales involved in the process. These processes can affect the multipolar structure of the source and consequently the produced gravitational wave. We present results of neutron star binary mergers both with and without magnetic field and discuss the magnetic effects on the gravitational waves, fluid structure, and merger timescale.   

Relativistic Radiation Magnetohydrodynamics in Dynamical Spacetimes

Many systems of current interest in relativistic astrophysics require a knowledge of radiative transfer in a magnetized fluid evolving in a strongly-curved, dynamical spacetime. Such systems include stellar core collapse, GRBs, binary NSNS and BHNS mergers, etc. To model these phenomena, all of which involve general relativity, radiation (either photons and/or neutrinos), and magnetohydrodynamics, we have developed a general relativistic code capable of evolving MHD fluids and radiation in dynamical spacetimes. Our code solves the coupled Einstein-Maxwell-MHD-Radiation system of equations both in axisymmetry and in full 3 + 1 dimensions. We evolve the metric by integrating the BSSN equations, and use a conservative, high-resolution shock-capturing scheme to evolve both the MHD and radiation moment equations. For our initial study, we treat optically thick gases and assume grey-body opacities. We perform a suite of tests to verify our code. In this talk, we summarize tests involving radiating shocks and nonlinear waves propagating in Minkowski spacetime with planar symmetry.   

Radiation Magnetohydrodynamics in Dynamical Spacetimes: `Thermal' Oppenheimer-Snyder Collapse

We have constructed a new general relativistic code capable of evolving magnetohydrodynamic fluids and radiation fields in a dynamical spacetime. In order to test our code's ability to handle radiation in a strong-field dynamical spacetime, we simulate the collapse from rest of a spherical dust ball, slightly perturbed by a small fluctuation of thermal radiation. For a sufficiently small perturbation, the matter and metric evolve according to an Oppenheimer-Snyder solution, while the radiation propagates according to the general relativistic diffusion approximation. Adopting a grey-body opacity law, and an optically thick medium, we evolve the metric, hydrodynamics and radiation fields self-consistently using our new code. We find good agreement between the numerical result and the analytic solution.   

Large-scale relativistic simulations in the characteristic approach

We report on high-resolution computations in the characteristic approach to numerical relativity, using an extensible, highly scalable computational framework (LEO). A combination of a multi-bloc decomposition of the sphere (the ``cubed sphere''), with spin raising and lowering (``eth'') operators on non-conformal coordinates, and a first order reduction of the Einstein equations is used to obtain a stable, globally second-order accurate numerical method. Applying the framework to a scalar field minimally coupled to gravity in three dimensions, we extract quasi-normal modes, and notice the appearance of energy saturation effects. We analyze the scaling properties of the underlying framework and discuss possible extensions.   

Close encounters of three black holes

We present the first fully relativistic longterm numerical evolutions of three equal- mass black holes in a hierarchical system consisting of a third black hole in orbit about a black-hole binary at twice the binaries separation. We find that these close-three- black-hole systems can have very different merger dynamics than black-hole binaries. In particular, we see distinctive waveforms, a suppression of the emitted gravitational radiation, and a redistribution of the energy of the system that can impart substantial kicks to one of the members of the binary. We evolve two such configurations and find very different behaviors. In one configuration the binary is quickly disrupted and the individual holes follow complicated trajectories and merge with the third hole in rapid succession, while in the other, the binary completes a half-orbit before the initial merger of one of the members with the third black hole, and the resulting two-black- hole system forms a highly elliptical, well separated binary that shows no significant inspiral for (at least) the first t~1000M of evolution.   

Small scale structure in the approach to the singularity

Numerical simulations are performed of the approach to a general spacetime singularity. In these simulations small scale structure forms on surfaces of codimension 1. The simulations are done with adaptive mesh refinement that resolves the small scale structure. The shape of the small scale structure is compared to an approximate formula for that shape.   

Numerical Simulations of Oscillatons: Excited States in Spherical Symmetry and Ground State Evolutions in 3D

Oscillatons are nonsingular solutions of the Einstein-Klein-Gordon equations represented by periodic metric and real field. Using a 1D code we find that spherically symmetric S-branch excited state oscillatons are inherently unstable under radial perturbations: they either migrate to the ground state or collapse to black holes. Similar to boson stars higher excited state oscillatons cascade through intermediate excited states during their migration to the ground state. Ground state oscillatons are then studied with a 3D numerical relativity code based on the Cactus Computational Toolkit. Finding the appropriate gauge condition for the dynamic oscillatons is challenging. Slicing conditions are explored and a customized gauge condition is implemented. The behavior of these stars under small nonradial perturbations is studied and gravitational waveforms are extracted. The gravitational waves damp on a short timescale, enabling us to obtain the complete waveform. This work is a starting point for the study of real scalar field systems in 3D.   

Physical characteristics of numerical apparent horizons

We present analytical results which enable the physical characterization of numerical apparent horizons. In particular, we introduce quantities which invariantly characterize the rate at which an apparent horizon is evolving and how close it is to either equilibrium or extremality. The definition of extremality does not require the apparent horizon to be either stationary or rotationally symmetric but does reduce to the standard notion for Kerr.