Covariant gravitational dynamics in 3+1+1 dimensions

Abstract

We develop a 3+1+1 covariant formalism with cosmological and astrophysical applications. First we give the evolution and constraint equations both on the brane and off-brane in terms of 3-space covariant kinematical, gravito-electro-magnetic (Weyl) and matter variables. We discuss the junction conditions across the brane in terms of the new variables. Then we establish a closure condition for the equations on the brane. We also establish the connection of this formalism with isotropic and anisotropic cosmological brane-worlds. Finally we derive a new brane solution in the framework of our formalism: the tidal charged Taub-NUT-(A)dS brane, which obeys the closure condition.

35 pages 1 fig; significantly expanded with (a) new closure condition on the brane, (b) discussion of anisotropic brane-worlds, (c) stationary vacuum space-times with local rotational symmetry including (d) a new tidal charged Taub-NUT-(A)dS brane solution; published version.