In this paper, we characterize the spacelike, the timelike and the null rectifying curves in the Minkowski 3-space in terms of centrodes. In particular, we show that the spacelike and timelike rectifying curves are the extremal curves for which the corresponding function takes its extremal value. On the other hand, we also show that the null rectifying curves are not the extremal curves and giv...

In this paper we develop a Morse Theory for timelike geodesics parameterized by a constant multiple of proper time. The results are obtained using an extension to the timelike case of the relativistic Fermat Principle, and techniques from Global Analysis on infinite dimensional manifolds. In the second part of the paper we discuss a limit process that allows to obtain also a Morse theory for li...

A bstract We propose a definition of asymptotic flatness at timelike infinity in four spacetime dimensions. present detailed study the equations motion and action supertranslations on fields. show that Lee-Wald symplectic form Ω( g, δ 1 g , 2 ) does not get contributions from future with our boundary conditions. As result, “future charges” can be computed any two-dimensional surface surrounding...

We show differentiability of a class of Geroch’s volume functions on globally hyperbolic manifolds. Furthermore, we prove that every volume function satisfies a local anti-Lipschitz condition over causal curves, and that locally Lipschitz time functions which are locally antiLipschitz can be uniformly approximated by smooth time functions with timelike gradient. Finally, we prove that in stably...

Basic theoretical issues relating to the response of confined relativistic particles are considered including the scaling of the response in spacelike and timelike regions of momentum transfer and the role of final state interactions. A simple single particle potential model incorporating relativity and linear confinement is solved exactly and its response is calculated. The response is studied...

We discuss plane wave backgrounds of string theory and their relation to Gödel–like universes. This involves a twisted compactification along the direction of propagation of the wave, which induces closed timelike curves. We show, however, that no such curves are geodesic. The particle geodesics and the preferred holographic screens we find are qualitatively different from those in the Gödel–li...

Abstract We seek S-brane solutions in D = 11 supergravity which can be characterized by a harmonic function H on the flat transverse space. It turns out that the Einstein’s equations force H to be a linear function of the transverse coordinates. The codimension one H = 0 hyperplane can be spacelike, timelike or null and the spacelike case reduces to the previously obtained SM2 or SM5 brane solu...

We study a class of timelike weakly extremal surfaces in flat Minkowski space R, characterized by the fact that they admit a C parametrization (in general not an immersion) of a specific form. We prove that if the distinguished parametrization is of class C, then the surface is regularly immersed away from a closed singular set of euclidean Hausdorff dimension at most 1 + 1/k, and that this bou...

Using the previously gained insight about the particle/field relation in conformal quantum field theories which required interactions to be related to the existence of particle-like states associated with fields which necessarily have an anomalous contribution in addition to their canonical scale-dimensions, we set out to construct a classification theory for the spectra of anomalous dimensions...