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Late-time tails of wave maps coupled to gravity

Piotr Bizoń1, Tadeusz Chmaj2,3, Andrzej Rostworowski1 and Stanisław Zając2

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We consider the late-time asymptotic behavior for solutions of Einstein's equations with the wave map matter. Using the third-order perturbation expansion about the flat spacetime we show that solutions starting from small compactly supported ℓ-equivariant initial data with ℓ ≥ 1 decay as t−(2ℓ+2) at future timelike infinity and as u−(ℓ+1) at future null infinity.


PACS

04.20.Jb Exact solutions

04.40.-b Self-gravitating systems; continuous media and classical fields in curved spacetime

04.20.Ha Asymptotic structure

MSC

83C75 Space-time singularities, cosmic censorship, etc.

83C30 Asymptotic procedures (radiation, news functions, H-spaces, etc.)

83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)

83C15 Exact solutions

Subjects

Gravitation and cosmology

Dates

Issue 22 (21 November 2009)

Received 17 June 2009, in final form 6 September 2009

Published 23 October 2009



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