Involutive Spacetime Distributions and p-Brane Dynamics

Details Involutive Spacetime Distributions and p-Brane Dynamics Involutive Spacetime Distributions and p-Brane Dynamics

1997-07-14

arxiv.org/abs/physics/9707013v1

Physics

Mathematical Physics

25 pages, LaTeX

Scientific paper

We propose a precise definition of multidimensional fluids generated by self-gravitating extended objects such as strings and membranes: a p-dimensional perfect fluid is a smooth involutive p-dimensional distribution on a spacetime, each integral manifold of which is a timelike, connected, immersed submanifold of dimension, p -- representing the history of a (p-1)-dimensional extended object. This geometric formulation of perfect fluids of higher dimensions naturally leads to the associated stress-energy tensor. Furthermore, the laws of temporal evolution and symmetries of such systems are derived, in general, from the Einstein field equations and the integrability conditions. We also present a matter model based on a 2-dimensional involutive distribution, and it is shown that the stress-energy tensor for self-gravitating strings gives rise to a non-trivial spherically symmetric spacetime with a naked singularity.

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