Lowest order covariant averaging of a perturbed metric and of the Einstein tensor

Details Lowest order covariant averaging of a perturbed metric and of the Einstein tensor Lowest order covariant averaging of a perturbed metric and of the Einstein tensor

2009-04-27

arxiv.org/abs/0904.4213v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages

Scientific paper

We present an explicit averaging formula in lowest order. Besides an arbitrary smearing function it contains two integrals of this function. This is necessary in order to achieve covariance. There is no need to solve any equations. In three dimensions the same averaging formula yields a covariant averaging of the Einstein tensor and thus of the field equations. We also present a simple extension to static perturbations in four dimensions. Various further extensions of the formalism appear possible.

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