Matching of spacetimes theory applied to rotating stars and quadratic gravity

233 p.Este resumen contiene un repaso breve de las actividades de investigación que se han llevado a cabo durante el desarrollo de la presente tesis doctoral, realizada con la ayuda predoctoral del Gobierno Vasco (BFI-2011-250) durante los años 2012-2015 en el departamento de Física Teórica e Historia de la Ciencia de la UPV/EHU, bajo la dirección de R.Vera. La primera parte del resumen está dedicada a explicar los problemas que se han abordado, cómo se ha hecho o qué métodos se han empleado y qué resultados hemos obtenido

Hartle's model within the general theory of perturbatiye matchings: the change in mass

Hartle's model provides the most widely used analytic framework to describe isolated compact bodies rotating slowly in equilibrium up to second order in perturbations in the context of General Relativity. Apart from some explicit assumptions, there are some implicit, like the "continuity" of the functions in the perturbed metric across the surface of the body. In this work we sketch the basics for the analysis of the second order problem using the modern theory of perturbed matchings. In particular, the result we present is that when the energy density of the fluid in the static configuration does not vanish at the boundary, one of the functions of the second order perturbation in the setting of the original work by Hartle is not continuous. This discrepancy affects the calculation of the change in mass of the rotating star with respect to the static configuration needed to keep the central energy density unchanged

First order perturbations of hypersurfaces of arbitrary causal character

In this work we study the problem of first order perturbations of a general hypersurface, i.e. with arbitrary causal character at each point. We extend the framework by Mars (Class. Quantum Grav. 22 3325 (2005)) where this problem was studied to second order for everywhere timelike or spacelike hypersurfaces, and we adapt it to cover the general case. We apply the formalism to the matching of spacetimes across a general hypersurface to first order in perturbation theory.Comment: 31 pages + appendices, 2 figure