Application of the Campbell-Magaard theorem to higher-dimensional physics

Stated succinctly, the original version of the Campbell-Magaard theorem says that it is always possible to locally embed any solution of 4-dimensional general relativity in a 5-dimensional Ricci-flat manifold. We discuss the proof of this theorem (and its variants) in n dimensions, and its application to current theories that postulate that our universe is a 4-dimensional hypersurface Sigma_0 within a 5-dimensional manifold, such as Space-Time-Matter (STM) theory and the Randall & Sundrum (RS) braneworld scenario. In particular, we determine whether or not arbitrary spacetimes may be embedded in such theories, and demonstrate how these seemingly disparate models are interconnected. Special attention is given to the motion of test observers in 5 dimensions, and the circumstances under which they are confined to Sigma_0. For each 5-dimensional scenario considered, the requirement that observers be confined to the embedded spacetime places restrictions on the 4-geometry. For example, we find that observers in the thin braneworld scenario can be localized around the brane if its total stress-energy tensor obeys the 5-dimensional strong energy condition. As a concrete example of some of our technical results, we discuss a Z_2 symmetric embedding of the standard radiation-dominated cosmology in a 5-dimensional vacuum.Comment: Typos corrected, 13 pages, no figures, two column forma

CP-odd weak basis invariants and texture zeros

We construct the CP-odd weak basis invariants from the neutrino mass matrix in a weak basis in which the charged lepton mass matrix is diagonal and find the necessary and sufficient conditions for CP conservation. We study the interrelationships between different CP-odd weak basis invariants to examine their implications for the Dirac and Majorana type CP violating phases for the phenomenologically allowed Frampton-Glashow-Marfatia texture zero structures of the neutrino mass matrix.Comment: 9 pages, three tables, Phys. Rev. D (to appear

Constraints on Weakly Mixed Sterile Neutrinos in the Light of SNO Salt Phase and 766.3 Ty KamLAND Data

The possibility of flavor transitions into sterile neutrinos (accompanying the dominant LMA transitions) in the solar boron neutrino flux has been examined in a scenario proposed by Hollanda and Smirnov to overcome some generic problems of the pure LMA scenario. It is found that the most recent SNO salt phase solar neutrino data and the KamLAND 766.3 Ty spectral data, allow for a significant sterile presence in the solar boron neutrino flux reaching the earth.Comment: 12 pages, 4 figure

Neutrino Parameter Space for a Vanishing eeee Element in the Neutrino Mass Matrix

The consequences of a texture zero at the $ee$ entry of neutrino mass matrix in the flavor basis, which also implies a vanishing effective Majorana mass for neutrinoless double beta decay, have been studied for Majorana neutrinos. The neutrino parameter space under this condition has been constrained in the light of all available neutrino data including the CHOOZ bound on $s_{13}^{2}$.Comment: 10 pages, 4 eps figures, typographical errors corrected, version to appear in Mod. Phys. Lett.