Starting from 2D Euclidean quantum gravity, we show that one recovers 2D Lorentzian quantum gravity by removing all baby universes. Using a peeling procedure to decompose the discrete, triangulated geometries along a one-dimensional path, we explicitly associate with each Euclidean space-time a (generalized) Lorentzian spacetime. This motivates a map between the parameter spaces of the two theo...

In the following Bell gives an account of the Lorentzian interpretation of relativistic effects, in which the Lorentz transformations are explained by a dynamical mechanism (including the assumption of an – though undetectable – aether) rather than derived from postulates as in the approach of Einstein. Bell concludes that teaching relativity can benefit from what he calls a “Lorentzian pedagog...

We develop a suitable generalization of Almgren’s theory of varifolds in a lorentzian setting, focusing on area, first variation, rectifiability, compactness and closure issues. Motivated by the asymptotic behaviour of the scaled hyperbolic Ginzburg-Landau equations, and by the presence of singularities in lorentzian minimal surfaces, we introduce, within the varifold class, various notions of ...

We show that positivity of energy for stationary, asymptotically flat, non-singular domains of outer communications is a simple corollary of the Lorentzian splitting theorem. A milestone in mathematical general relativity is the positive energy theorem [8, 10]. It is somewhat surprising that the standard proofs of this result do not have anything to do with Lorentzian geometry. In this note we ...

‎We study curvature properties of four-dimensional Lorentzian manifolds with two-symmetry property‎. ‎We then consider Einstein-like metrics‎, ‎Ricci solitons and homogeneity over these spaces‎‎.

There is strong evidence coming from Lorentzian dynamical triangulations that the unboundedness of the gravitational action is no obstacle to the construction of a well-defined non-perturbative path integral. In a continuum approach, a similar suppression of the conformal divergence comes about as the result of a non-trivial path-integral measure. The progress of the last few years has establis...