Codimension Two Branes and Distributional Curvature

Abstract

In general relativity, there is a well-developed formalism for working with the approximation that a gravitational source is concentrated on a shell, or codimension one surface. By contrast, there are obstacles to concentrating sources on surfaces that have a higher codimension, for example, a string in a spacetime with dimension greater than or equal to four. Here it is shown that, by giving up some of the generality of the codimension one case, curvature can be concentrated on submanifolds that have codimension two. A class of metrics is identified such that (1) the scalar curvature and Ricci densities exist as distributions with support on a co-dimension two submanifold, and (2) using the Einstein equation, the distributional curvature corresponds to a concentrated stress-energy with equation of state p equals minus the energy density, where p is the isotropic pressure tangent to the submanifold. This is the appropriate stress-energy to describe a self-gravitating brane that is governed by an area action, or a brane world deSitter cosmology. The possibility of having a different equation of state arise from a wider class of metrics is discussed.

18 pages; v2 references added; typos corrected, references added; additional references added

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Cited by in corpus (5)

• Notes on the Two-brane Model with Variable Tension
• Cosmic branes and asymptotic structure
• Induced vacuum energy-momentum tensor in the background of a cosmic string
• Gravitational constraints of dS branes in AdS Einstein-Brans-Dicke bulk
• The End of the Road for Bulk Fields in Warped Randall-Sundrum Braneworlds