Oihane F. Blanco

• Ph. D. in Mathematics and Physics
• Professor (Full) at Universidad San Francisco de Quito

In this work we will focus on the causal character of Carter Spacetime (see B. Carter, Causal structure in space-time, Gen. Rel. Grav. 1 4 337-406, 1971). The importance of this spacetime is the following: for the causally best well behaved spacetimes (the globally hyperbolic ones), there are several characterizations or alternative definitions. In...

En esta investigación nos enfocamos en el carácter causal del espaciotiempo de Carter (ver [2], [10]). Este espaciotiempo es importante por la siguiente razón: para los espaciotiempos con un comportamiento causal óptimo, es decir, los globalmente hiperbólicos, existen varias caracterizaciones o definiciones alternativas. En algunos casos se ha demo...

Second-order symmetric Lorentzian spaces, that is to say, Lorentzian manifolds with vanishing second derivative of the curvature tensor R, are characterized by several geometric properties, and explicitly presented. Locally, they are a product M=M_1 x M_2 where each factor is uniquely determined as follows: M_2 is a Riemannian symmetric space and M...

We give a summary of recent results on the explicit local form of the second-order symmetric Lorentzian manifolds in arbitrary dimension, and its global version. These spacetimes turn out to be essentially a specific subclass of plane waves.

As a difference with the positive-definite Riemannian case, in the Lorentzian case there exists proper second-order symmetric spacetimes, i.e., those with vanishing second covariant derivative of the Riemannian tensor ($R_{\lambda\mu\nu\rho;\alpha;\beta}=0$) which are not locally symmetric ($R_{\lambda\mu\nu\rho;\alpha}\neq 0$). In fact, they lie i...