Authors: Carlos Castro
After reviewing the basic ideas behind Born's Reciprocal Relativity theory, the geometry of the (co) tangent bundle of spacetime is studied via the introduction of nonlinear connections associated with certain $nonholonomic$ modifications of Riemann--Cartan gravity within the context of Finsler geometry. The curvature tensors in the (co) tangent bundle of spacetime are explicitly constructed leading to the analog of the Einstein vacuum field equations. The geometry of Hamilton Spaces associated with curved phase spaces follows. An explicit construction of a gauge theory of gravity in the $8D$ co-tangent bundle $ T^*M$ of spacetime is provided, and based on the gauge group $ SO (6, 2) \times_s R^8$ which acts on the tangent space to the cotangent bundle $ T_{ ( x, p) } T^*M $ at each point $ ({\bf x}, {\bf p})$. Several gravitational actions associated with the geometry of curved phase spaces are presented. We conclude with a discussion about the geometrization of matter, QFT in accelerated frames, {\bf T}-duality, double field theory, and generalized geometry.
Comments: 20 Pages. Submitted to IJMPA
Download: PDF
[v1] 2015-09-21 01:53:02
Unique-IP document downloads: 195 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.