Título/Title: Non-singular cosmologies à la Palatini.

Autor/Author: Gonzalo J. Olmo

Abstract: I will discuss how modifications of Einstein's theory using the Palatini formalism can lead to the resolution of the big bang singularity in several cases of interest.

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Título/Title: Palatini f(R) and Extended Palatini f(R,Q) Black Holes with Electric charge.

Autor/Author: Diego Rubiera-García (Universidad de Oviedo )

Abstract: We study electrically charged black holes in f(R) and f(R,Q) theories formulated à la Palatini, i.e. by assuming the metric and connection to be independent entities. We show that in the f(R) case, electromagnetic theories with vanishing trace (as Maxwell theory) itself produces the same equations of motion as those of General Relativity (GR), which motivates us to consider non-linear extensions (non-linear electrodynamics). We show how the structure of GR-Born-Infeld black holes is modified near the center in terms of internal horizons and how the central singularities could be ameliorated. In the f(R,Q) we show that Maxwell theory already produces different results from those of GR, and we find different kinds of structures including regular black holes (singularity-free) and regular cores.

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