Topological Methods in Nonlinear Analysis

On lifespan of solutions to the Einstein equations

Piotr Bogusław Mucha

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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.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 29, Number 1 (2007), 181-198.

Dates
First available in Project Euclid: 13 May 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1463144892

Mathematical Reviews number (MathSciNet)
MR2308221

Zentralblatt MATH identifier
1136.83007

Citation

Mucha, Piotr Bogusław. On lifespan of solutions to the Einstein equations. Topol. Methods Nonlinear Anal. 29 (2007), no. 1, 181--198. https://projecteuclid.org/euclid.tmna/1463144892


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