47 research outputs found
Interpretation of quantal manifolds
In quantum gravity, one looks for alternative structures to spacetime physics
than ordinary real manifolds. Here, we propose an alternative universal
construction containing the latter as an equilibrium state under the action of
the universal diffeomorphism group. Our theory contains many other previous
proposals in the literature as special cases. However, the crucial point we
make is that those have to be appreciated in the universal context developed
here.Comment: 16 pages. arXiv admin note: substantial text overlap with
arXiv:1101.511
A new topology on the space of Lorentzian metrics on a fixed manifold
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 relative to two space time points and and metrics and . 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.Comment: 33 page
The limit space of a Cauchy sequence of globally hyperbolic spacetimes
In this second paper, I construct a limit space of a Cauchy sequence of
globally hyperbolic spacetimes. In the second section, I work gradually towards
a construction of the limit space. I prove the limit space is unique up to
isometry. I als show that, in general, the limit space has quite complicated
causal behaviour. This work prepares the final paper in which I shall study in
more detail properties of the limit space and the moduli space of (compact)
globally hyperbolic spacetimes (cobordisms). As a fait divers, I give in this
paper a suitable definition of dimension of a Lorentz space in agreement with
the one given by Gromov in the Riemannian case.Comment: 31 pages, 5 figures, submitted to Classical and Quantum gravity,
seriously improved presentatio