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arXiv · 1211.2994

Geometrization of Mass in General Relativity

Nasser Boroojerdian
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Abstract

In this paper we will extend the notion of tangent bundle to a $\z$ graded tangent bundle. This graded bundle has a Lie algebroid structure and we can develop notions semi-riemannian metrics, Levi-civita connection, and curvature, on it. In case of space-times manifolds, even part of the tangent bundle is related to space and time structures(gravity) and odd part is related to mass distribution in space-time. In this structure, mass becomes part of the geometry, and Einstein field equation can be reconstructed in a new simpler form. The new field equation is purely geometric.

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Nasser Boroojerdian. 2012-11-13. Geometrization of Mass in General Relativity. https://doi.org/10.1007/s10773-013-1530-6

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