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Register a new userNumerical Relativity As A Tool For Computational Astrophysics
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The astrophysics of compact objects, which requires Einsteins theory of general relativity for understanding phenomena such as black holes and neutron stars, is attracting increasing attention. In general relativity, gravity is governed by an extremely complex set of coupled, nonlinear, hyperbolic-elliptic partial differential equations. The largest parallel supercomputers are finally approaching the speed and memory required to solve the complete set of Einsteins equations for the first time since they were written over 80 years ago, allowing one to attempt full 3D simulations of such exciting events as colliding black holes and neutron stars. In this paper we review the computational effort in this direction, and discuss a new 3D multi-purpose parallel code called ``Cactus for general relativistic astrophysics. Directions for further work are indicated where appropriate.
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We describe and present the first observational evidence that light propagating near a rotating black hole is twisted in phase and carries orbital angular momentum. The novel use of this physical observable as an additional tool for the previously known techniques of gravitational lensing allows us to directly measure, for the first time, the spin parameter of a black hole. With the additional information encoded in the orbital angular momentum, not only can we reveal the actual rotation of the compact object, but we can also use rotating black holes as probes to test General Relativity.
We discuss a general formalism for numerically evolving initial data in general relativity in which the (complex) Ashtekar connection and the Newman-Penrose scalars are taken as the dynamical variables. In the generic case three gauge constraints and twelve reality conditions must be solved. The analysis is applied to a Petrov type {1111} planar spacetime where we find a spatially constant volume element to be an appropriate coordinate gauge choice.
This document proposes data formats to exchange numerical relativity results, in particular gravitational waveforms. The primary goal is to further the interaction between gravitational-wave source modeling groups and the gravitational-wave data-analysis community. We present a simple and extendable format which is applicable to various kinds of gravitational wave sources including binaries of compact objects and systems undergoing gravitational collapse, but is nevertheless sufficiently general to be useful for other purposes.
We present the recent results of a research project aimed at constructing a robust wave extraction technique for numerical relativity. Our procedure makes use of Weyl scalars to achieve wave extraction. It is well known that, with a correct choice of null tetrad, Weyl scalars are directly associated to physical properties of the space-time under analysis in some well understood way. In particular it is possible to associate $Psi_4$ with the outgoing gravitational radiation degrees of freedom, thus making it a promising tool for numerical wave--extraction. The right choice of the tetrad is, however, the problem to be addressed. We have made progress towards identifying a general procedure for choosing this tetrad, by looking at transverse tetrads where $Psi_1=Psi_3=0$. As a direct application of these concepts, we present a numerical study of the evolution of a non-linearly disturbed black hole described by the Bondi--Sachs metric. This particular scenario allows us to compare the results coming from Weyl scalars with the results coming from the news function which, in this particular case, is directly associated with the radiative degrees of freedom. We show that, if we did not take particular care in choosing the right tetrad, we would end up with incorrect results.
The gauge polyvalence of a new numerical code is tested, both in harmonic-coordinate simulations (gauge-waves testbed) and in singularity-avoiding coordinates (simple Black-Hole simulations, either with or without shift). The code is built upon an adjusted first-order flux-conservative version of the Z4 formalism and a recently proposed family of robust finite-difference high-resolution algorithms. An outstanding result is the long-term evolution (up to 1000M) of a Black-Hole in normal coordinates (zero shift) without excision.
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