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In spacetimes of dimension greater than four it is natural to consider higher order (in $R)$ corrections to the Einstein equations. In this paper generalized Israel junction conditions for a membrane in such a theory are derived. This is achieved by generalizing the Gibbons-Hawking boundary term. The junction conditions are applied to simple brane world models, and are compared to the many contradictory results in the literature.
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Stephen C. Davis (2003) studied this question.
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