New models for extreme gravitational systems

A large number of classes of modified theories of gravity have been developed for a long time. They have attracted much attention from physicists, since they show different aspects concerning gravitational interaction. In fact, these aspects may extend the role of gravity not only at large scales but at microscopic regimes, so that they have been systematically related to fundamental issues such as the occurrence of space-time singularities, the loss of renormalizability or the origin of the accelerated expansion of the universe, among others. Despite the successful predictions and the highly tested accuracy of General Relativity (GR) in describing the gravitational phenomena, the absence of an appropriate explanation for these issues has stimulated the investigation of new alternative models of gravitation.The extension of the conventional approach can be addressed by the introduction into the gravitational action of higher order corrections depending on the metric tensor alone. Such a procedure preserves the geometric structure of the space-time and potentially yields new propagating degrees of freedom related to metric, which means that not only the phenomenological compatibility with GR must be considered by the new framework but also the viability of its stability conditions. On the other hand, it is also possible to define a more complex geometry by the modification of the affine connection...