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Journal Article

#### The Taylor expansion at past time-like infinity

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##### Fulltext (public)

1306.5626.pdf

(Preprint), 403KB

CMP324_263.pdf

(Any fulltext), 471KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

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.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-B411-F

##### 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 $p$.