Essentials of Classical Brane Dynamics
Brandon Carter

TL;DR
This paper provides a comprehensive overview of the geometry and dynamics of relativistic brane models, including their kinematic properties and equations of motion, relevant for understanding point particles, strings, membranes, and brane world scenarios.
Contribution
It offers a detailed geometric and dynamical framework for relativistic branes, including their curvature properties and tensorial equations of motion, extending previous models to arbitrary dimensions.
Findings
Geometry of brane worlds described by fundamental tensors.
Brane evolution governed by tensorial equations involving stress and curvature.
Free branes follow simple tensorial equations with no external forces.
Abstract
This article provides a self contained overview of the geometry and dynamics of relativistic brane models, of the category that includes point particle, string, and membrane representations for phenomena that can be considered as being confined to a worldsheet of the corresponding dimension (respectively one, two, and three) in a thin limit approximation in an ordinary 4 dimensional spacetime background. This category also includes ``brane world'' models that treat the observed universe as a 3-brane in 5 or higher dimensional background. The first sections are concerned with purely kinematic aspects: it is shown how, to second differential order, the geometry (and in particular the inner and outer curvature) of a brane worldsheet of arbitrary dimension is describable in terms of the first, second, and third fundamental tensor. The later sections show how -- to lowest order in the thin…
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Cosmology and Gravitation Theories · Noncommutative and Quantum Gravity Theories
