A method by which a geometry with causality violation can be taken as a part of a globally causal space-time model is presented. This procedure is applied to a pair of extensions to Godel s space-time: a “Godel-generalized” and a stringlike solution. The latter is shown to be an intermediate region between Godel and deformed […]

## Metric Relativity and the Dynamical Bridge: Highlights of Riemannian Geometry in Physics

We present an overview of recent developments concerning modifications of the geometry of space-time to describe various physical processes of interactions among classical and quantum configurations. We concentrate in two main lines of research: the Metric Relativity and the Dynamical Bridge. We describe the notion of equivalent (dragged) metric gμν which is responsible to map […]

## Extended Born-Infeld theory and the bouncing magnetic universe

We show that a generalized Born-Infeld electrodynamics responsible for regular configurations of the static field of a charged particle produces a nonsingular universe that contains a bouncing. This means that the Universe has a previous collapsing phase, attains a minimum value for its scale factor and then enters into an expanding phase. We exhibit such […]

## Bouncing cosmologies

We review the general features of nonsingular universes (i.e. those that go from an era of accelerated collapse to an expanding era without displaying a singularity) as well as cyclic universes. We discuss the mechanisms behind the bounce, and analyze examples of solutions that implement these mechanisms. Observational consequences of such regular cosmologies are also […]

## Beyond analog gravity: the case of exceptional dynamics

We show that it is possible to go beyond the propagation aspects usually contemplated in the analog models of gravity. Until now, the emergence of a metric appears in the description of excitations around a given background solution or in the study of field discontinuities in the geometrical optics regime. We now overcome some limitations […]