Extra Force from an Extra Dimension: Comparison Between Brane Theory, SpaceTimeMatter Theory, and Other Approaches
Abstract
We investigate the question of how an observer in 4D perceives the fivedimensional geodesic motion. We consider the interpretation of null and nonnull bulk geodesics in the context of brane theory, spacetimematter theory (STM) and other noncompact approaches. We develop a ``frameinvariant'' formalism that allows the computation of the rest mass and its variation as observed in 4D. We find the appropriate expression for the fouracceleration and thus obtain the extra force observed in 4D. Our formulae extend and generalize all previous results in the literature. An important result here is that the extra force in braneworld models with Z_{2}symmetry is continuous and well defined across the brane. This is because the momentum component along the extra dimension is discontinuous across the brane, which effectively compensates the discontinuity of the extrinsic curvature. We show that brane theory and STM produce identical interpretation of the bulk geodesic motion. This holds for null and nonnull bulk geodesics. Thus, experiments with test particles are unable to distinguish whether our universe is described by the brane world scenario or by STM. However, they do discriminate between the brane/STM scenario and other noncompact approaches. Among them the canonical and embedding approaches, which we examine in detail here.
 Publication:

General Relativity and Gravitation
 Pub Date:
 June 2004
 DOI:
 10.1023/B:GERG.0000022391.57597.3b
 Bibcode:
 2004GReGr..36.1335D