A new topology on the space of Lorentzian metrics on a fixed manifold

Details A new topology on the space of Lorentzian metrics on a fixed manifold A new topology on the space of Lorentzian metrics on a fixed manifold

2011-04-10

arxiv.org/abs/1104.1811v1

Class. Quantum Grav. 19 (2002) 6075-6107

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

33 pages

Scientific paper

10.1088/0264-9381/19/23/313

We give a covariant definition of closeness between (time oriented) Lorentzian metrics on a manifold M, using a family of functions which measure the difference in volume form on one hand and the difference in causal structure relative to a volume scale on the other hand. These functions will distinguish two geometric properties of the Alexandrov sets $ A(p,q), \tilde{A} (p,q) $ relative to two space time points $q$ and $p$ and metrics $g$ and $ \tilde{g} $. It will be shown that this family generates uniformities and consequently a topology on the space of Lorentzian metrics which is Hausdorff when restricted to strongly causal metrics. This family of functions will depend on parameters for a volume scale, a length scale (relative to the volume scale) and an index which labels a submanifold with compact closure of the given manifold M.

Affiliated with

Also associated with

No associations

Rating

A new topology on the space of Lorentzian metrics on a fixed manifold does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A new topology on the space of Lorentzian metrics on a fixed manifold, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A new topology on the space of Lorentzian metrics on a fixed manifold will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-57929