Newton's law modifications due to a Sol manifold extra dimensional space

Using Globular Clusters to Test Newtons Law of Gravity

New measurements of the velocity dispersion of the globular cluster ω Centauri allow to trace its gravitational potential down to an acceleration of 8 × 10 cm s. It is found that the dispersion profile remains flat well inside the tidal radius as soon as the acceleration of gravity approaches a0, a result that finds its simplest explanation within the contest of MOND. A similar behavior is obse...

ar X iv : 0 80 1 . 35 27 v 2 [ he p - th ] 1 6 Se p 20 08 Corrections to Gravity due to a Sol Manifold Extra Dimensional Space

The corrections to the gravitational potential due to a Sol extra dimensional compact manifold, denoted as M 3 A , are studied. The total spacetime is of the form M 4 × M 3 A. The range of the Sol corrections is investigated and compared to the range of the T 3 corrections. We find that for small values of the radius of the extra dimensions (R < 10 −6) the range of the Sol manifold corrections ...

ar X iv : 0 80 1 . 35 27 v 1 [ he p - th ] 2 3 Ja n 20 08 Corrections to Gravity due to a Sol Manifold Extra Dimensional Space

The corrections to the gravitational potential due to a Sol extra dimensional compact manifold, denoted as M 3 A , are studied. The total spacetime is of the form M 4 × M 3 A. The range of the Sol corrections is investigated and compared to the range of the T 3 corrections.

On images of continuous functions from a compact manifold to Euclidean space

GROUPOID ASSOCIATED TO A SMOOTH MANIFOLD

‎In this paper‎, ‎we introduce the structure of a groupoid associated to a vector field‎ ‎on a smooth manifold‎. ‎We show that in the case of the $1$-dimensional manifolds‎, ‎our‎ ‎groupoid has a‎ ‎smooth structure such that makes it into a Lie groupoid‎. ‎Using this approach‎, ‎we associated to‎ ‎every vector field an equivalence‎ ‎relation on the Lie algebra of all vector fields on the smooth...