A manifestly covariant equation is derived to describe the second order perturbations in topological defects and membranes on arbitrary curved background spacetimes. This, on one hand, generalizes work on macroscopic strings in Minkowski spacetime an
d introduces a framework for studing in a precise manner membranes behavior near the black hole horizon and on the other hand, introduces a more general framework for examining the stability of topological defects in curved spacetimes.
The phenomenon of neutrino oscillations is studied usually as a mixing between the flavor neutrinos and the neutrinos having a definite mass. The mixing angles and the mass eigenvalues are treated independently in order to accommodate the experimenta
l data. We suggest that neutrino oscillations are connected to the structure of spacetime. We expand on a recently proposed model, where two mirror branes coexist. One brane hosts left-handed particles (our brane), while the other brane hosts right-handed particles. Majorana-type couplings mixes neutrinos in an individual brane, while Dirac-type couplings mixes neutrinos across the brares. We first focus our attention in a single brane. The mass matrix, determined by the Majorana mass, leads to mass eigenstates and further to mixing angles identical to the mixing angles proposed by the tri-bimaximal mixing. When we include the Dirac-type coupling, connecting the two branes, we obtain a definite prediction for the transition to a sterile neutrino (right-handed neutrino). With m_L (m_R) the Majorana mass for the left (right) brane, we are able to explain the solar and the atmospheric neutrino data with m_L = 2m_R and m_R = 10**(-2) eV.
