arXiv subjects

Wai-Mo Suen

Publications and source records attributed to Wai-Mo Suen.

At least 37 records · Page 2Linked to original sources

arXiv1998

Event Horizons in Numerical Relativity II: Analyzing the Horizon

We present techniques and methods for analyzing the dynamics of event horizons in numerically constructed spacetimes. There are three classes of analytical tools we have investigated. The first class consists of proper geometrical measures of the horizon which allow us comparison with perturbation theory and powerful global theorems. The second class involves the location and study of horizon generators. The third class includes the induced horizon 2-metric in the generator comoving coordinates and a set of membrane-paradigm like quantities. Applications to several distorted, rotating, and colliding black hole spacetimes are provided as examples of these techniques.

gr-qc↗

arXiv1997

Dynamical Evolution of Boson Stars II: Excited States and Self-Interacting Fields

The dynamical evolution of self-gravitating scalar field configurations in numerical relativity is studied. The previous analysis on ground state boson stars of non-interacting fields is extended to excited states and to fields with self couplings. Self couplings can significantly change the physical dimensions of boson stars, making them much more astrophysically interesting (e.g., having mass of order 0.1 solar mass). The stable ($S$) and unstable ($U$) branches of equilibrium configurations of boson stars of self-interacting fields are studied; their behavior under perturbations and their quasi-normal oscillation frequencies are determined and compared to the non-interacting case. Excited states of boson stars with and without self-couplings are studied and compared. Excited states also have equilibrium configurations with $S$ and $U$ branch structures; both branches are intrinsically unstable under a generic perturbation but have very different instability time scales. We carried out a detailed study of the instability time scales of these configurations. It is found that highly excited states spontaneously decay through a cascade of intermediate states similar to atomic transitions.

gr-qc↗

arXiv1997

Newtonian and post-Newtonian binary neutron star mergers

We present two of our efforts directed toward the numerical analysis of neutron star mergers, which are the most plausible sources for gravitational wave detectors that should begin operating in the near future. First we present Newtonian 3D simulations including radiation reaction (2.5PN) effects. We discuss the gravitational wave signals and luminosity from the merger with/without radiation reaction effects. Second we present the matching problem between post-Newtonian formulations and general relativity in numerical treatments. We prepare a spherical, static neutron star in a post-Newtonian matched spacetime, and find that discontinuities at the matching surface become smoothed out during fully relativistic evolution if we use a proper slicing condition.

gr-qc↗

arXiv1996

The Near-Linear Regime of Gravitational Waves in Numerical Relativity

We report on a systematic study of the dynamics of gravitational waves in full 3D numerical relativity. We find that there exists an interesting regime in the parameter space of the wave configurations: a near-linear regime in which the amplitude of the wave is low enough that one expects the geometric deviation from flat spacetime to be negligible, but nevertheless where nonlinearities can excite unstable modes of the Einstein evolution equations causing the metric functions to evolve out of control. The implications of this for numerical relativity are discussed.

gr-qc↗

arXiv1996

Dynamics of Gravitational Waves in 3D: Formulations, Methods, and Tests

The dynamics of gravitational waves is investigated in full 3+1 dimensional numerical relativity, emphasizing the difficulties that one might encounter in numerical evolutions, particularly those arising from non-linearities and gauge degrees of freedom. Using gravitational waves with amplitudes low enough that one has a good understanding of the physics involved, but large enough to enable non-linear effects to emerge, we study the coupling between numerical errors, coordinate effects, and the nonlinearities of the theory. We discuss the various strategies used in identifying specific features of the evolution. We show the importance of the flexibility of being able to use different numerical schemes, different slicing conditions, different formulations of the Einstein equations (standard ADM vs. first order hyperbolic), and different sets of equations (linearized vs. full Einstein equations). A non-linear scalar field equation is presented which captures some properties of the full Einstein equations, and has been useful in our understanding of the coupling between finite differencing errors and non-linearites. We present a set of monitoring devices which have been crucial in our studying of the waves, including Riemann invariants, pseudo-energy momentum tensor, hamiltonian constraint violation, and fourier spectrum analysis.

gr-qc↗

arXiv1996

Coordinate Conditions and Their Implementation in 3D Numerical Relativity

We put forth a few ideas on coordinate conditions and their implementation in numerical relativity. Coordinate conditions are important for the long time scale simulations of relativistic systems, e.g., for the determination of gravitational waveforms from astrophysical events to be measured by LIGO/VIRGO. We demonstrate the importance of, and propose methods for, the {\it active enforcement} of coordinate properties. In particular, the constancy of the determinant of the spatial 3-metric is investigated as such a property. We propose an exceedingly simple but powerful idea for implementing elliptic coordinate conditions that not only makes possible the use of complicated elliptic conditions, but is also {\it orders of magnitude} more efficient than existing methods for large scale 3D simulations.

gr-qc↗

arXiv1995

Head-on collision of two black holes: comparison of different approaches

A benchmark problem for numerical relativity has been the head-on collision of two black holes starting from the ``Misner initial data,'' a closed form momentarily stationary solution to the constraint equations with an adjustable closeness parameter $μ_0$. We show here how an eclectic mixture of approximation methods can provide both an efficient means of determining the time development of the initial data and a good understanding of the physics of the problem. When the Misner data is chosen to correspond to holes initially very close together, a common horizon surrounds both holes and the geometry exterior to the horizon can be treated as a non-spherical perturbation of a single Schwarzschild hole. When the holes are initially well separated the problem can be treated with a different approximation scheme, ``the particle-membrane method.'' For all initial separations, numerical relativity is in principle applicable, but is costly and of uncertain accuracy. We present here a comparison of the different approaches. We compare waveforms, for $\ell=2$ and $\ell=4$ radiation, for different values of $μ_0$, from the three different approaches to the problem.

gr-qc↗

arXiv1995

Three dimensional numerical relativity: the evolution of black holes

We report on a new 3D numerical code designed to solve the Einstein equations for general vacuum spacetimes. This code is based on the standard 3+1 approach using cartesian coordinates. We discuss the numerical techniques used in developing this code, and its performance on massively parallel and vector supercomputers. As a test case, we present evolutions for the first 3D black hole spacetimes. We identify a number of difficulties in evolving 3D black holes and suggest approaches to overcome them. We show how special treatment of the conformal factor can lead to more accurate evolution, and discuss techniques we developed to handle black hole spacetimes in the absence of symmetries. Many different slicing conditions are tested, including geodesic, maximal, and various algebraic conditions on the lapse. With current resolutions, limited by computer memory sizes, we show that with certain lapse conditions we can evolve the black hole to about $t=50M$, where $M$ is the black hole mass. Comparisons are made with results obtained by evolving spherical initial black hole data sets with a 1D spherically symmetric code. We also demonstrate that an ``apparent horizon locking shift'' can be used to prevent the development of large gradients in the metric functions that result from singularity avoiding time slicings. We compute the mass of the apparent horizon in these spacetimes, and find that in many cases it can be conserved to within about 5\% throughout the evolution with our techniques and current resolution.

gr-qc↗

arXiv1994

Horizon Boundary Condition for Black Hole Spacetimes

It was recently shown that spacetime singularities in numerical relativity could be avoided by excising a region inside the apparent horizon in numerical evolutions. In this paper we report on the details of the implementation of this scheme. The scheme is based on using (1)~a horizon locking coordinate which locks the coordinate system to the geometry, and (2)~a finite differencing scheme which respects the causal structure of the spacetime. We show that the horizon locking coordinate can be affected by a number of shift conditions, such as a ``distance freezing'' shift, an ``area freezing'' shift, an ``expansion freezing'' shift, or the minimal distortion shift. The causal differencing scheme is illustrated with the evolution of scalar fields, and its use in evolving the Einstein equations is studied. We compare the results of numerical evolutions with and without the use of this horizon boundary condition scheme for spherical black hole spacetimes. With the boundary condition a black hole can be evolved accurately well beyond $t=1000 M$, where $M$ is the black hole mass.

gr-qc↗

arXiv1994

Event Horizons in Numerical Relativity I: Methods and Tests

This is the first paper in a series on event horizons in numerical relativity. In this paper we present methods for obtaining the location of an event horizon in a numerically generated spacetime. The location of an event horizon is determined based on two key ideas: (1) integrating backward in time, and (2) integrating the whole horizon surface. The accuracy and efficiency of the methods are examined with various sample spacetimes, including both analytic (Schwarzschild and Kerr) and numerically generated black holes. The numerically evolved spacetimes contain highly distorted black holes, rotating black holes, and colliding black holes. In all cases studied, our methods can find event horizons to within a very small fraction of a grid zone.

gr-qc↗

arXiv1994

Singularity Avoidance in Numerical Black Hole Spacetimes

Spacetime singularities in numerical relativity can be avoided by excising a region of the computational domain from inside the apparent horizon. We report on results of such a scheme that is based on using ({\it i}) a horizon locking coordinate which locks the coordinate system to the geometry, and ({\it ii}) a finite differencing scheme which respects the causal structure of the spacetime. With this technique a black hole can be evolved accurately well beyond $t=1000M$, where $M$ is the black hole mass.

gr-qc↗

arXiv1994

Event Horizons of Numerical Black Holes

We have developed a powerful and efficient method for locating the event horizon of a black hole spacetime, making possible the study of the dynamics of event horizons in numerical relativity. We describe the method and apply it to a colliding black hole spacetime.

gr-qc↗

arXiv1994

A 3D Apparent Horizon Finder

We report on an efficient method for locating the apparent horizon in numerically constructed dynamical 3D black hole spacetimes. Instead of solving the zero expansion partial differential equation, our method uses a minimization procedure. Converting the PDE problem to minimization eliminates the difficulty of imposing suitable boundary conditions for the PDE. We demonstrate the effectiveness of this method in both 2D and 3D cases. The method is also highly parallelizable for implementation in massively parallel computers.

gr-qc↗

arXiv1994

3D Numerical Relativity at NCSA

Numerical relativity is finally coming of age with the development of massively parallel computers. 3D problems, which were completely intractable several years ago due to limited computer power, can now be performed with grid sizes of about $200^3$. We report on several new codes developed for solving the full 3D Einstein equations, and present results of using them to evolve black holes and gravitational waves.

gr-qc↗

arXiv1994

Formation gf Bosonic Compact Objects

We showed that compact bosonic objects can be formed through a process we called gravitational cooling. A central issue in the subject of boson star is whether a classical field configuration, {\it e.g.,} one described by the Klein-Gordon equation, can collapse to form a compact star-like object, as there is apparently no dissipation in the Klein-Gordon equation. We demonstrated that there IS an efficient cooling mechanism to get rid of the kinetic energy for the formation of a compact object purely through the gravitational coupling, a mechanism universal to all self-graviting fields. Implications of this mechanism are discussed, including the abundance of bosonic stars in the universe, and the possibility of ruling out the axion as a dark matter condidate.

gr-qc↗

arXiv1994

The Head-On Collision of Two Equal Mass Black Holes: Numerical Methods

The head-on collision of two nonrotating axisymmetric equal mass black holes is treated numerically. We take as initial data the single parameter family of time-symmetric solutions discovered by Misner which consists of two Einstein-Rosen bridges that can be placed arbitrarily distant from one another. A number of problems associated with previous attempts to evolve these data sets have been overcome. In this article, we discuss our choices for coordinate systems, gauges, and the numerical algorithms that we have developed to evolve this system.

gr-qc↗

arXiv1994

The Head-On Collision of Two Equal Mass Black Holes Peter Anninos

We study the head-on collision of two equal mass, nonrotating black holes. Various initial configurations are investigated, including holes which are initially surrounded by a common apparent horizon to holes that are separated by about $20M$, where $M$ is the mass of a single black hole. We have extracted both $\ell = 2$ and $\ell=4$ gravitational waveforms resulting from the collision. The normal modes of the final black hole dominate the spectrum in all cases studied. The total energy radiated is computed using several independent methods, and is typically less than $0.002 M$. We also discuss an analytic approach to estimate the total gravitational radiation emitted in the collision by generalizing point particle dynamics to account for the finite size and internal dynamics of the two black holes. The effects of the tidal deformations of the horizons are analysed using the membrane paradigm of black holes. We find excellent agreement between the numerical results and the analytic estimates.

gr-qc↗

arXiv1994

Dynamics of Apparent and Event Horizons

The dynamics of apparent and event horizons of various black hole spacetimes, including those containing distorted, rotating and colliding black holes, are studied. We have developed a powerful and efficient new method for locating the event horizon, making possible the study of both types of horizons in numerical relativity. We show that both the event and apparent horizons, in all dynamical black hole spacetimes studied, oscillate with the quasinormal frequency.

gr-qc↗