Is perturbation theory misleading in general relativity?

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Abstract
Two senses in which the perturbation equations of general relativity can be misleading are explored. (i) Under certain circumstances there exist solutions of the perturbation equations that appear to be gauge, in that the metric perturbation is the symmetrized derivative of a vector field, but which nonetheless are not true gauge. (ii) Under certain circumstances there exist solutions of the perturbation equations that cannot, even locally, be extended to higher order in perturbation theory. The latter is a local version of the well-known phenomenon of ‘‘linearization instability.’’

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