Aspects of General Relativity: Pseudo-Finsler extensions, Quasi-normal frequencies and Multiplication of tensorial distributions

This thesis is based on three different projects, all of them are directly linked to the classical general theory of relativity, but they might have consequences for quantum gravity as well. The first chapter deals with pseudo-Finsler geometric extensions of the classical theory, these being ways of naturally representing high-energy Lorentz symmetry violations. The second chapter deals with the problem of highly damped quasi-normal modes related to different types of black hole spacetimes. Besides the astrophysical meaning of the quasi-normal modes, there are conjectures about the link between the highly damped modes and black hole thermodynamics. The third chapter is related to the topic of multiplication of tensorial distributions.Comment: PhD thesis, 207 page

Quasinormal modes for the scattering on a naked Reissner-Nordstrom singularity

What should be the quasinormal modes associated with a spacetime that contains a naked singularity instead of a black hole? In the present work we address this problem by studying the scattering of scalar fields on a curved background described by a Reissner-Nordstr\"om spacetime with $|q| > m$. We show that there is a qualitative difference between cases with $1 < q^2/m^2 \lesssim 9/8$ and cases with $q^2/m^2 \gtrsim 9/8$. We discuss the necessary conditions for the well-posedness of the problem, and present results for the low damped modes in the low $l$ and large $l$ limit. We also consider the asymptotically highly damped quasinormal modes. We present strong evidence that such modes are absent in the case of a naked Reissner-Nordstr\"om singularity, corroborating recent conjectures relating them to classical and quantum properties of horizons.Comment: v3: final version to appear in Physical Review D, 17 pages, 10 figures, v3: only minor cosmetic changes (few typos corrected) with respect to v2, v1: the same physics, but missing one sectio