New variables for brane-world gravity

Abstract

Geometric variables naturally occurring in a time-like foliation of brane-worlds are introduced. These consist of the induced metric and two sets of lapse functions and shift vectors, supplemented by two sets of tensorial, vectorial and scalar variables arising as projections of the two extrinsic curvatures. A subset of these variables turn out to be dynamical. Brane-world gravitational dynamics is given as the time evolution of these variables.