Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2005-02-09
Class. Quantum Grav. 22, 1143-1166 (2005)
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
22 pages, to appear in Class. Quantum Grav. 22
Scientific paper
10.1088/0264-9381/22/6/015
This paper is concerned exclusively with axisymmetric spacetimes. We want to develop reductions of Einstein's equations which are suitable for numerical evolutions. We first make a Kaluza-Klein type dimensional reduction followed by an ADM reduction on the Lorentzian 3-space, the (2+1)+1 formalism. We include also the Z4 extension of Einstein's equations adapted to this formalism. Our gauge choice is based on a generalized harmonic gauge condition. We consider vacuum and perfect fluid sources. We use these ingredients to construct a strongly hyperbolic first-order evolution system and exhibit its characteristic structure. This enables us to construct constraint-preserving stable outer boundary conditions. We use cylindrical polar coordinates and so we provide a careful discussion of the coordinate singularity on axis. By choosing our dependent variables appropriately we are able to produce an evolution system in which each and every term is manifestly regular on axis.
Rinne Oliver
Stewart John M.
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