Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-11-07
Class.Quant.Grav. 19 (2002) 827
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
submitted to Classical and Quantum Gravity; stability analysis of a maximal slicing gauge is corrected
Scientific paper
10.1088/0264-9381/19/4/314
We present a general approach to the analysis of gauge stability of 3+1 formulations of General Relativity (GR). Evolution of coordinate perturbations and the corresponding perturbations of lapse and shift can be described by a system of eight quasi-linear partial differential equations. Stability with respect to gauge perturbations depends on a choice of gauge and a background metric, but it does not depend on a particular form of a 3+1 system if its constrained solutions are equivalent to those of the Einstein equations. Stability of a number of known gauges is investigated in the limit of short-wavelength perturbations. All fixed gauges except a synchronous gauge are found to be ill-posed. A maximal slicing gauge and its parabolic extension are shown to be ill-posed as well. A necessary condition is derived for well-posedness of metric-dependent algebraic gauges. Well-posed metric-dependent gauges are found, however, to be generally unstable. Both instability and ill-posedness are associated with perturbations of physical accelerations of reference frames.
Khokhlov Alexei M.
Novikov Igor D.
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