On lifespan of solutions to the Einstein equations
Keywords
Einstein equations, hyperbolic system, existence of maximal solutions, initial value problem, domains of dependenceAbstract
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.Downloads
Published
2007-03-01
How to Cite
1.
MUCHA, Piotr Bogusław. On lifespan of solutions to the Einstein equations. Topological Methods in Nonlinear Analysis. Online. 1 March 2007. Vol. 29, no. 1, pp. 181 - 198. [Accessed 25 April 2024].
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