Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-10-19
Phys.Rev.D77:023524,2008
Physics
High Energy Physics
High Energy Physics - Theory
REVTEX4, 7 pages, 1 figure
Scientific paper
10.1103/PhysRevD.77.023524
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. We formulate the appropriate junction conditions on the brane. We prove the equivalence of both theories. In particular, we prove the equivalence of the junction conditions with different assumptions related to the continuity of the metric along the brane.
Balcerzak Adam
Dabrowski Mariusz P.
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