Johan Noldus 2002 Class. Quantum Grav. 19 6075 doi:10.1088/0264-9381/19/23/313
A new topology on the space of Lorentzian metrics on a fixed manifold
Johan Noldus
Show affiliationsWe 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, on the other, the difference in causal structure relative to a volume scale. These functions will distinguish two geometric properties of the Alexandrov sets A(p, q), 
(p, q) relative to two spacetime points q and p and metrics g 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, length scale (relative to the volume scale) and an index which labels a submanifold with compact closure of the given manifold M.
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Issue 23 (7 December 2002)
Received 7 June 2002, in final form 30 August 2002
Published 11 November 2002
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A new topology on the space of Lorentzian metrics on a fixed manifold
Johan Noldus 2002 Class. Quantum Grav. 19 6075
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