Joint linearization instabilities in general relativity

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Abstract
When Einstein’s equations are supplemented by symmetry conditions, linearization instabilities can occur that are not present in either of the two sets of equations. The general conditions for this joint instability are investigated. This is illustrated with an example where both the Einstein equations and the flatness condition have more linearized solutions than exact solutions. In a minisuperspace model the geometrical reason for these instabilities is shown.

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