In this note a proof is given for local existence and uniqueness of minimal surfaces with the topology of the halfplane respectively a cylinder of Lorentzian type with values in certain Lorentzian manifolds for given initial values up to the first derivatives. Global existence is proved for the case that the target manifold is diffeomorphic to Rn.

Abstract. Imaginary time is often used in quantum tunnelling calculations. This article advocates a conceptually sounder alternative: complex lapse. In the “3+1” action for the Einstein gravitational field minimally coupled to a Klein-Gordon field, allowing the lapse function to be complex yields a complex action which generates both the usual Lorentzian theory and its Riemannian analogue, and ...

In this paper we present results for the wave-vector dependent shear viscosity for a model atomic fluid with short ranged repulsive interactions computed by molecular dynamics simulations. It is shown that the data can be fitted to two different simple functional forms over a large density range, namely, a function composed of two Gaussian terms and a Lorentzian type function with a variable wa...

In these lecture notes, I describe the motivation behind a recent formulation of a non-perturbative gravitational path integral for Lorentzian (instead of the usual Euclidean) space-times, and give a pedagogical introduction to its main features. At the regularized, discrete level this approach solves the problems of (i) having a welldefined Wick rotation, (ii) possessing a coordinate-invariant...

We analyse the quantum geometry of 3-dimensional deformed special relativity (DSR) and the notion of spacetime points in such a context, identified with coherent states that minimize the uncertainty relations among spacetime coordinates operators. We construct this system of coherent states in both the Riemannian and Lorentzian case, and study their properties and their geometric interpretation.

All the entire solutions to the maximal surface equation in certain 3-dimensional Lorentzian manifolds, obeying the null energy condition, are obtained. Thus, we solve new Calabi–Bernstein problems. As a consequence, the corresponding parametric versions are also given. The behaviour of this Calabi– Bernstein property with respect to an special family of C2-perturbations of Lorentz–Minkowski sp...

In this paper I present a spacetime of two open universes connected by a Lorentzian wormhole. The spacetime has the following features: (1) It can exactly solve the Einstein equations; (2) The weak energy condition is satisfied everywhere; (3) It has a topology of R2 × Tg (g ≥ 2); (4) It has no event horizons.

We identify a fundamental obstruction to any theory of the beginning of the Universe, formulated as a semiclassical path integral. The Hartle-Hawking no boundary proposal and Vilenkin's tunneling proposal are examples of such theories. Each may be formulated as the quantum amplitude for obtaining a final 3-geometry by integrating over 4-geometries. We introduce a new mathematical tool-Picard-Le...

Starting from the space of Lorentzian metrics, we examine the full gravitational path integral in 3 and 4 space-time dimensions. Inspired by recent results obtained in a regularized, dynamically triangulated formulation of Lorentzian gravity, we gaugefix to proper-time coordinates and perform a non-perturbative “Wick rotation” on the physical configuration space. Under certain assumptions about...