General Relativity by Kawaguchi geometry
1 Department of Mathematics, Torino University, via Carlo Alberto 10, 10123 Torino, Italy
2 Department of Algebra and Geometry, Faculty of Science, Palacky University, 17. listopadu 12, 771 46 Olomouc, Czech Republic
3 Physics Department, Ochanomizu University, 2-1-1 Ootsuka Bunkyo, Tokyo, Japan
a e-mail: email@example.com
Published online: 5 September 2013
We construct a parameterisation invariant Lagrange theory of fields up to second order by using multivector bundles and Kawaguchi geometry. In this setup, the spacetime is an dynamical object which is a submanifold of the greater manifold, and the actual spacetime is the solution of Euler-Lagrange equations. Such theory is a reasonable mathematical foundation to describe an extended theory of Einstein’s general relativity, and is capable of being a stage for unification with other physical fields.
© Owned by the authors, published by EDP Sciences, 2013
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 2.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.