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2007

Generalized Israel Junction Conditions for a Fourth-Order Brane World

Balcerzak, Adam, Dabrowski, Mariusz P.

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We discuss a general fourth-order theory of gravity on the brane.

In general, the formulation of the junction conditions (except for Euler characteristics such as Gauss-Bonnet term) leads to the higher powers of the delta function and requires regularization.
We suggest the way to avoid such a problem by imposing the metric and its first derivative to be regular at the brane, while the second derivative to have a kink, the third derivative of the metric to have a step function discontinuity, and no sooner as the fourth derivative of the metric to give the delta function contribution to the field equations.
Alternatively, we discuss the reduction of the fourth-order gravity to the second-order theory by introducing an extra tensor field.

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