Brane Waves

In brane-world cosmology gravitational waves can propagate in the higher dimensions (i.e., in the ‘bulk’). In some appropriate regimes the bulk gravitational waves may be approximated by plane waves. We systematically study five-dimensional gravitational waves that are algebraically special and of type N. In the most physically relevant case the projected non-local stress tensor on the brane is formally equivalent to the energy-momentum tensor of a null fluid. Some exact solutions are studied to illustrate the features of these branes. More importantly, it is possible that these bulk gravitational plane waves may act as initial conditions for the gravitational field in the bulk, thereby enabling the field equations to be integrated on the brane. In brane-world cosmology, matter fields and gauge interactions are confined to a four-dimensional brane moving in a higher-dimensional “bulk” spacetime. This paradigm is motivated by string and M-theory; in particular, generalized Randall-Sundrum-type models [1] are relatively simple phenomenological fivedimensional (5D) models which capture some of the essential features of the dimensional reduction of Hořava-Witten theory [2]. In a recent analysis of the asymptotic dynamical evolution of perfect fluid brane-world cosmological models close to the initial singularity, it was found that for an appropriate range of the equation of state parameter an isotropic singularity is a past-attractor [3]. It was subsequently argued that the initial cosmological singularity is isotropic in brane-world cosmological models. The 5D field equations are GAB = −Λ5 gAB + κ 2 5 TAB , Λ5 = − 6 l2 . (1) The projected field equations on the brane are [4]: Gμν = −Λgμν + κ Tμν + 6 κ λ Sμν − Eμν , (2) [email protected] [email protected]