A framework for large-scale relativistic simulations in the characteristic approach

Details A framework for large-scale relativistic simulations in the characteristic approach A framework for large-scale relativistic simulations in the characteristic approach

2007-11-05

arxiv.org/abs/0711.0564v1

Phys.Rev.D76:124029,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

RevTeX4, 22 pages, 21 figures, to appear in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.76.124029

We present a new computational framework (LEO), that enables us to carry out the very first large-scale, high-resolution computations in the context of the characteristic approach in numerical relativity. At the analytic level, our approach is based on a new implementation of the ``eth'' formalism, using a non-standard representation of the spin-raising and lowering angular operators in terms of non-conformal coordinates on the sphere; we couple this formalism to a partially first-order reduction (in the angular variables) of the Einstein equations. The numerical implementation of our approach supplies the basic building blocks for a highly parallel, easily extensible numerical code. We demonstrate the adaptability and excellent scaling of our numerical code by solving, within our numerical framework, for a scalar field minimally coupled to gravity (the Einstein-Klein-Gordon problem) in 3-dimensions. The nonlinear code is globally second-order convergent, and has been extensively tested using as reference a calibrated code with the same boundary-initial data and radial marching algorithm. In this context, we show how accurately we can follow quasi-normal mode ringing. In the linear regime, we show energy conservation for a number of initial data sets with varying angular structure. A striking result that arises in this context is the saturation of the flow of energy through the Schwarzschild radius. As a final calibration check we perform a large simulation with resolution never achieved before.

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