We describe the general class of N -extended D = (2 + 1) Galilean supersymmetries obtained, respectively, from the N -extended D = 3 Poincaré superalgebras with maximal sets of central charges. We confirm the consistency of supersymmetry with the presence of the 'exotic' second central charge θ. We show further how to introduce a N = 2 Galilean superfield equation describing nonrelativistic spin 0 and spin 1 2 free particles.
We discuss the problem of the motion of classical strings in some black hole and cosmological spacetimes. In particular, the null string limit (zero tension) of tensile strings is considered. We present some new exact string solutions in Reissner-Nordström black hole background as well as in the Einstein Static Universe and in the Einstein-Schwarzschild (a black hole in the Einstein Static Universe) spacetime. These solutions can give some insight into a general nature of propagation of strings (cosmic and fundamental) in curved backgrounds.
We study the extensions of DGP model which are described by five-dimensional Einstein gravity coupled covariantly to 3-brane with induced gravity term and consider warped D=4 de Sitter background field solutions on the brane. The case with included D=5 AdS cosmological term is also considered. Following background field method we obtain the field equations described by the Lagrangean terms bilinear in gravitational field. In such a linear field approximation on curved dS background we calculate explicitly the five-dimensional massive terms as well as the mass-like ones on the brane. We investigate the eigenvalue problem of Schrödinger-like equation in fifth dimension for graviton masses and discuss the existence of massless as well as massive graviton modes in the bulk and on the brane without and with induced gravity. * Supproted by KBN grant 1P03B 01828
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