| dc.description.abstract | This thesis discusses several questions related to the local existence of
the characteristic initial value problem (CIVP) in general relativity (GR)
First, we study the CIVP of vacuum Einstein field equations by using
Newman-Penrose (NP) formalism. Working in a gauge suggested by
Stewart, and following the strategy taken in the work of Luk, we demonstrate
local existence of solutions in a neighbourhood of the set on which
data are given. These data are given on intersecting null hypersurfaces.
Existence near their intersection is achieved by combining the observation
that the field equations are symmetric hyperbolic in this gauge
with the results of Rendall. To obtain existence all the way along the
null-hypersurfaces themselves, a bootstrap argument involving the NP
variables is performed.
Second, applying the same strategy, we analyze the asymptotic CIVP
for the conformal Einstein field equations (CEFE) and demonstrate the
local existence of solutions in a neighbourhood of the set on which the
data are given. In particular, we obtain existence of solutions along a
narrow rectangle along null infinity which, in turn, corresponds to an
infinite domain in the asymptotic region of the physical spacetime. This
result generalises work by K ann ar on the local existence of solutions to
the CIVP by means of Rendalls reduction strategy.
In the last part of the thesis, we make use of a CIVP for the CEFE to
provide an alternative proof of local extension of null infinity given by Li
and Zhu see [1]. This proof builds on the framework developed in first
two parts of the thesis. | en_US |
