On lifespan of solutions to the Einstein equations

Piotr Bogusław Mucha

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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