  I analyze the properties of thin shells through which the scalar curvature R
is discontinuous in gravity theories with R + R^2 Lagrangian on the bulk. These
shells/domain walls are of a new kind because they possess, in addition to the
standard energy-momentum tensor, an external energy flux vector, an external
scalar pressure/tension and, most exotic of all, another energy-momentum tensor
contribution resembling classical dipole distributions on a shell: a double
layer. I prove that all these contributions are necessary to make the entire
energy-momentum tensor divergence-free. This is the first known occurrence of
such a type of double layer allowed in a gravity theory. I present explicit
examples in constant-curvature 5-dimensional bulks, with a brief study of their
properties: new physical behaviors arise.
