Brane dynamics for treatment of cosmic strings and vortons

Abstract

This course provides a self contained introduction to the general theory 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. The first part of the course is 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 extension to a foliation by a congruence of such worldsheets is also briefly discussed. In the next part, it is shown how -- to lowest order in the thin limit -- the evolution of such a brane worldsheet will always be governed by a simple tensorial equation of motion whose left hand side is the contraction of the second fundamental tensor with the relevant surface stress tensor, while the right hand side will simply vanish in the case of free motion and will otherwise be just the orthogonal projection of any external force density that may happen to act on the brane. (Allowance for first order deviations from such a thin limit treatment would require evolution equations of a more complicated kind of which a prototype example is presented.) The last part of the course concentrates on the case of a string, and particularly on the stationary (centrifugally supported) configurations known as vortons, which, if they are sufficiently stable, may be of considerable cosmological significance.

arXiv comment89 pages Latex (colour). Tlaxcala lecture notes, 2nd Mexican School on Gravitation and Mathematical Physics, Dec.,1996, ed. A. Garcia, C. Lammerzahl, A. Macias, T. Matos, D. Nunez. Proceedings available on line from Science Network Publishing at "http://kaluza.physik.uni-konstanz.de/2MS/ProcMain.html"

References in corpus (12)

• Cosmic Vortons and Particle Physics Constraints
• Black Holes from Nucleating Strings
• Dynamical instability criterion for circular (vorton) string loops
• Curvature Corrections to Dynamics of Domain Walls
• Covariant perturbations of domain walls in curved spacetime
• Transonic Elastic Model for Wiggly Goto-Nambu String
• Avoidance of Collapse by Circular Current-Carrying Cosmic String Loops
• Spontaneous Current Generation in Cosmic Strings
• Radiative Backreaction on Global Strings
• Dynamical Stability of Witten Rings
• Wiggly Relativistic Strings
• Cosmic Electroweak Strings

Cited by in corpus (18)

• The exact numerical treatment of inflationary models
• How Fluids Bend: the Elastic Expansion for Higher-Dimensional Black Holes
• Stealth Branes
• Limits on Cosmic Chiral Vortons
• Newton-Cartan Submanifolds and Fluid Membranes
• An equation of state for purely kinetic k-essence inspired by cosmic topological defects
• String dynamics and ejection along the axis of a spinning black hole
• Constraints on the effective fluid theory of stationary branes
• Emission of gravitational waves by superconducting cosmic strings
• An orientifold of adS_5xT^11 with D7-branes, the associated alpha'^2- corrections and their role in the dual N=1 Sp(2N+2M)xSp(2N) gauge theory
• Generalized Formalism in Gauge-Invariant Gravitational Perturbations
• Self-Dual Cosmic Strings and Gravitating Vortices in Gauged Sigma Models
• T-duality of D-brane action at order ${\alpha }^{\prime }$ in bosonic string theory
• Topological terms and the global symplectic geometry of the phase space in string theory
• Low Velocity Gravitational Capture by Long Cosmic Strings
• Gravitational Capture and Scattering of Straight Test Strings with Large Impact Parameters
• Cosmic Microwave Background anisotropies generated by cosmic strings with small-scale structure
• Curvature relations in almost product manifolds