Gravity in curved phase-spaces, finsler geometry and two-times physics

Abstract:

The generalized (vacuum) field equations corresponding to gravity on curved 2d-dimensional (dim) tangent bundle/phase spaces and associated with the geometry of the (co)tangent bundle TM d-1, 1(T*M d-1, 1) of a d-dim spacetime M d-1, 1 are investigated following the strict distinguished d-connection formalism of LagrangeFinsler and HamiltonCartan geometry. It is found that there is no mathematical equivalence with Einstein's vacuum field equations in spacetimes of 2d dimensions, with two times, after a d+d KaluzaKlein-like decomposition of the 2d-dim scalar curvature R is performed and involving the introduction of a nonlinear connection A αμ(x μ, y b). The physical applications of the 4-dim phase space metric solutions found in this work, corresponding to the cotangent space of a 2-dim spacetime, deserve further investigation. The physics of two times may be relevant in the solution to the problem of time in quantum gravity and in the explanation of dark matter. Finding nontrivial solutions of the generalized gravitational field equations corresponding to the 8-dim cotangent bundle (phase space) of the 4-dim spacetime remains a challenging task. © 2012 World Scientific Publishing Company.

Año de publicación:

2012

Keywords:

• Gravity
• Finsler Geometry
• HamiltonCarten spaces
• Phase Space

Fuente:

scopus