On lifespan of solutions to the Einstein equations

Piotr Bogusław Mucha

DOI: http://dx.doi.org/10.12775/TMNA.2007.008

Abstract


We investigate the issue of existence of maximal solutions to the vacuum
Einstein solutions for asymptotically flat spacetime. Solutions are
established globally in time outside a domain of influence of a suitable large
compact set, where singularities can appear. Our approach shows existence of
metric coefficients which obey the following behavior:
$g_{\alpha\beta}=\eta_{\alpha\beta}+O(r^{-\delta})$ for a small fixed
$\delta > 0$ at infinity (where $\eta_{\alpha\beta}$ is the Minkowski metric).
The system is studied in the harmonic (wavelike) gauge.

Keywords


Einstein equations; hyperbolic system; existence of maximal solutions; initial value problem; domains of dependence

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