Conformal regularization of Einstein's field equations

Details Conformal regularization of Einstein's field equations Conformal regularization of Einstein's field equations

2005-04-14

arxiv.org/abs/gr-qc/0504063v2

Class.Quant.Grav. 22 (2005) 3775-3787

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

New title plus corrections and text added. To appear in CQG

Scientific paper

10.1088/0264-9381/22/17/026

To study asymptotic structures, we regularize Einstein's field equations by means of conformal transformations. The conformal factor is chosen so that it carries a dimensional scale that captures crucial asymptotic features. By choosing a conformal orthonormal frame we obtain a coupled system of differential equations for a set of dimensionless variables, associated with the conformal dimensionless metric, where the variables describe ratios with respect to the chosen asymptotic scale structure. As examples, we describe some explicit choices of conformal factors and coordinates appropriate for the situation of a timelike congruence approaching a singularity. One choice is shown to just slightly modify the so-called Hubble-normalized approach, and one leads to dimensionless first order symmetric hyperbolic equations. We also discuss differences and similarities with other conformal approaches in the literature, as regards, e.g., isotropic singularities.

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