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The Taylor expansion at past time-like infinity

Friedrich, H. (2013). The Taylor expansion at past time-like infinity. Communications in Mathematical Physics, 324, 263-300. doi:10.1007/s00220-013-1803-1.

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1306.5626.pdf (Preprint), 403KB
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Creators:
Friedrich, Helmut1, Author
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1Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24012

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Free keywords: General Relativity and Quantum Cosmology, gr-qc
Abstract: We study the initial value problem for the conformal field equations with data given on a cone ${\cal N}_p$ with vertex $p$ so that in a suitable conformal extension the point $p$ will represent past time-like infinity $i^-$, the set ${\cal N}_p \setminus \{p\}$ will represent past null infinity ${\cal J}^-$, and the freely prescribed (suitably smooth) data will acquire the meaning of the incoming {\it radiation field} for the prospective vacuum space-time. It is shown that: (i) On some coordinate neighbourhood of $p$ there exist smooth fields which satisfy the conformal vacuum field equations and induce the given data at all orders at $p$. The Taylor coefficients of these fields at $p$ are uniquely determined by the free data. (ii) On ${\cal N}_p$ there exists a unique set of fields which induce the given free data and satisfy the transport equations and the inner constraints induced on ${\cal N}_p$ by the conformal field equations. These fields and the fields which are obtained by restricting the functions considered in (i) to ${\cal N}_p$ coincide at all orders at $p$.

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Dates: 2013-06-242013
Publication Status: Published in print
Pages: 40 pages
Publishing info: -
Rev. Method: -
Identifiers: arXiv: 1306.5626
DOI: 10.1007/s00220-013-1803-1
Degree: -

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### Source 1

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Title: Communications in Mathematical Physics
Source Genre: Journal
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Publ. Info: Heidelberg : Springer-Verlag Heidelberg
Pages: - Volume / Issue: 324 Sequence Number: - Start / End Page: 263 - 300 Identifier: ISSN: 0010-3616
CoNE: /journals/resource/954925392313