Session Q20 - Gravitational Radiation - Theory and Numerical Relativity.
MIXED session, Monday afternoon, May 01
102A, LBCC

[Q20.001]

This abstract not available.

[Q20.002] Grazing Collision of Binary Black Holes I

The computational simulation of binary black hole mergers is a problem of great interest in general relativity. Such mergers are expected to be strong astrophysical sources of gravitational radiation measurable by gravitational wave detectors currently under construction around the world. Their accurate simulation via numerical solutions to the Einstein field equations will provide an understanding of the gravitational radiation that ensue from such events as well as provide a computational laboratory in which to study the physics of two body problems such as these in general relativity. We present recent results from numerical simulations of binary black hole mergers using black hole excision techniques. We discuss the initial data, excision techniques and algorithms and results from such a simulation. The eventual goal of this work is to be capable of long term evolutions of the merger phase through the ringdown phase.

[Q20.003] Grazing Collision of Binary Black Holes II: From Merger Towards Ringdown

One of the great challenges in gravitational physics is to simulate the collision of two black holes in order to study the resulting gravitational radiation. The Agave collaboration has successfully collided two spinning black holes in a grazing merger. The eventual goal of this work is to simulate the orbit, merger and ringdown stages of an astrophysical binary black hole system. The success of the grazing collision has proven to be strongly dependent on predicting the dynamics of the apparent horizons during the evolution. This is due to the fact that the region inside the apparent horizon containing the singularity is removed from the computational domain. Once the black holes have merged, one is left with a single black hole horizon. The spacetime is of a highly distorted black hole. We present results from simulations of the merged to ringdown stage in the life of a binary black hole collision. We show not only how crucial a role the dynamics of the apparent horizon plays in extending the lifetime of the simulation towards ringdown, but also the vital role the appropriate prescription of gauge conditions plays.

[Q20.004] Approximate Analytical Solutions to the Initial Value Problem of Black Hole Binary Systems

We present approximate analytical solutions to the Hamiltonian and momentum constraint equations, corresponding to systems composed of two black holes with arbitrary linear and angular momentum. The analytical nature of these solutions makes them easier to implement than the traditional numerical approach of solving the corresponding elliptic equations. We show that the methods developed here provide initial data whose violation of the constraint equations falls below the truncation error present in finite difference codes for a given range of grid resolutions. Thus these data are suitable for use in evolutionary codes. In this paper we examine the case of a head-on collision of two mass M black holes at a separation distance of 10M. For this case, we show that the approximate solutions are valid for a range of grid spacings as fine as h = M/8.

[Q20.005] Gravitational collapse in 2+1 dimensional AdS spacetime

We present results of numerical simulations of the formation of black holes from the gravitational collapse of a massless, minimally-coupled scalar field in 2+1 dimensional anti de-Sitter (AdS) spacetime. The vacuum (modulo a negative cosmological constant) or BTZ black hole solutions are interesting in that they can be constructed through topological identifications in AdS spacetime, and hence are spacetimes of constant curvature. We show that in the dynamical formation of BTZ black holes a curvature singularity develops at the origin. We also discuss our attempts to find critical behaviour at the threshold of black hole formation -- a task complicated by the finite light-crossing time of signals in AdS spacetime.

[Q20.006] BH-NS Simulations via characteristic evolutions

The characteristic formulation of the Einstein equations provides a rather unique tool for numerical relativity. It has been used recently to good effect in three dimensional evolutions of vacuum black hole using the concept of excision. In conjunction with hydrodynamical evolution one would hope to tackle a range of interesting astrophysical problems involving dynamic black holes. I will describe a collaborative work aimed in this direction.

[Q20.007] Numerical evolution of Brill waves

Numerical simulations are performed of the gravitational collapse of axisymmetric Brill waves. The dependence of the collapse process on both the amplitude and the shape of the initial wave is found.

[Q20.008] Instability of Rapidly Rotating Compact Stellar Cores

One interesting class of gravitational wave sources encompasses rapidly rotating stellar cores that have expended their nuclear fuel and are prevented from undergoing further collapse by centrifugal forces. The development of global rotational instabilities in such a ``centrifugally-hung'' object can produce gravitational radiation and may shed enough angular momentum to allow full collapse to a supernova.

We are using 3-D numerical simulations to investigate the stability of rotating stellar cores modeled as polytropes with N > 3 for various rotation laws. The hydrocode calculates the gravitational field in the Newtonian limit, and the resulting gravitational radiation is computed in the quadrupole approximation. In certain cases we find that such cores can be unstable at values of \beta = T/|W| considerably lower than the Maclaurin limit \beta_d \approx 0.27 for the dynamical bar instability.

[Q20.009] Three-dimensional adaptive evolutions of gravitational waves in numerical relativity

The first fully adaptive 3-D calculations of gravitational waves in numerical relativity are presented. We take a low amplitude Teukolsky wave as initial data, and evolve it using the conformal formalism on a 3-D Cartesian grid. An outgoing Sommerfeld-type boundary condition is imposed on the outer boundary of the grid. The PARAMESH package is used to manage the adaptive mesh refinement and parallel implementation of the code. Unigrid runs confirm second order convergence of the code. The (2-level) adaptive runs show good performance of the adaptive mesh refinement (AMR) code with both refinement and derefinement tracking the gravitational wave. We discuss some of the issues related to the AMR such as refinement criteria and high frequency numerical noise.

[Q20.010] Evolution of Rotating Supermassive Stars: Low-Viscosity Limit

Thermal emission from a rotating, supermassive star will cause the configuration to contract slowly and spin up. If internal viscosity and magnetic fields are sufficiently weak, the contracting star will rotate differentially. In this limit, the fate of a cooling supermassive star depends sensitively on its initial angular momentum distribution. If the star is nearly spherical and in uniform rotation initially, then cooling and contraction will cause it to flatten and spin up to the mass-shedding limit. Subsequent cooling may lead to mass and angular momentum loss which might eventually drive the configuration to the onset of dynamical collapse. However, for other initial profiles characterized by differential rotation, mass-shedding limits do not always exist along an evolutionary sequence. Instead, a supermassive star will encounter the dynamical bar-mode instability, which may trigger the growth of nonaxisymmetric bars. Either scenario may lead to the generation of long wavelength gravitational waves, which could be detectable by future space-based laser interferometers like LISA.

[Q20.011] Gravitational Radiation Damping and the Three Body Problem

A two body planar Kepler system with the included post- Newtonian effect of gravitational radiation damping will eventually spiral inward toward collapse. If the additional perturbation due to a third mass is included one sees evidence of passage through resonance with numerical integration. This results in the semi-major axis of the Kepler system staying fixed on average through the duration of the passage through resonance. The resonance is between the period of the Kepler orbit and the period of the third mass' orbit around the binary. In this study, a simple model is developed which describes the motion of the binary subject to gravitational radiation damping and the influence of a third mass. The method of averaging is used to study the equations of motion. Second order partial averaging is used to examine the behavior of the system near resonance.

Part Q of program listing