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Tetrad formalism for numerical relativity on conformally compactified constant mean curvature hypersurfaces
 

Summary: Tetrad formalism for numerical relativity on conformally
compactified constant mean curvature hypersurfaces
James M. Bardeen,1
Olivier Sarbach,2
and Luisa T. Buchman3
1
Physics Department, University of Washington, Seattle, Washington 98195 USA
2
Instituto de Fi´sica y Matema´ticas, Universidad Michoacana de San Nicola´s de Hidalgo,
Edificio C-3, Ciudad Universitaria, 58040 Morelia, Michoaca´n, Me´xico
3
Theoretical Astrophysics, California Institute of Technology, Pasadena, California 91125 USA
(Received 28 January 2011; published 24 May 2011)
We present a new evolution system for Einstein's field equations which is based on tetrad fields and
conformally compactified hyperboloidal spatial hypersurfaces which reach future null infinity. The boost
freedom in the choice of the tetrad is fixed by requiring that its timelike leg be orthogonal to the foliation,
which consists of constant mean curvature slices. The rotational freedom in the tetrad is fixed by the 3D
Nester gauge. With these conditions, the field equations reduce naturally to a first-order constrained
symmetric hyperbolic evolution system which is coupled to elliptic equations for the gauge variables. The
conformally rescaled equations are given explicitly, and their regularity at future null infinity is discussed.

  

Source: Adolphs, Ralph - Psychology and Neuroscience, California Institute of Technology

 

Collections: Biology and Medicine