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The moduli space of isometry classes of globally hyperbolic spacetimes

This paper is part of a research programme on the structure of the moduli space of Lorentzian geometries, a Lorentzian analogue of Gromov–Hausdorff theory based on the use of the Lorentz distance as…
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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, on the…
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A Lorentzian Gromov–Hausdorff notion of distance

This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov?Hausdorff distance…
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Lorentzian Manifolds and Causal Sets as Partially Ordered Measure Spaces

We consider Lorentzian manifolds as examples of partially ordered measure spaces, sets endowed with compatible partial order relations and measures, in this case given by the causal structure and the…
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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 section 2, I work gradually towards a construction of the limit space. I prove that the…
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Foundations of a theory of quantum gravity

A logically consistent and precise theory of quantum gravity is presented that automatically incoorporates an extended form of gravity as well as a quantum gauge theory and is to a high degree Whiteheadian.
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A Proof of the Falsity of the Axiom of Choice.

We observe two things in this paper : namely that the Banach Tarski paradox is false and that the correct part of the proof leads to a violation of the axiomof choice.

A Higher Language for Mathematics.

This work extends the language of mathematics by generalizing the logical implication and negation and serves as an extension of intuitionistic logic.

Rebuttal on “anti-gravitation” by S. Hossenfelder

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0 30 80 74 v 3 1 8 N ov 2 00 3 A Lorentzian Gromov-Hausdorff notion of distance

This paper is the first of three in which I study the moduli space of isometry classes of (compact) globally hyperbolic spacetimes (with boundary). I introduce a notion of Gromov-Hausdorff distance…
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