New variables for brane-world gravity

TL;DR

This paper introduces new geometric variables derived from a time-like foliation of brane-worlds, providing a framework for describing brane-world gravitational dynamics through their evolution.

Contribution

It defines a comprehensive set of geometric variables, including induced metrics, lapse functions, shift vectors, and extrinsic curvature projections, to formulate brane-world gravity dynamics.

Findings

Identifies which variables are dynamical.

Provides a new formalism for brane-world gravitational evolution.

Lays groundwork for future analytical and numerical studies.

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.