Μελέτη προτύπων μεμβρανών συνδιάστασης μεγαλύτερης από 1 και εξέταση της ευστάθειάς τους κάτω από βαρυτικές διαταραχές

Abstract

In this thesis we discuss codimension-2 braneworlds and the existence of black holes on the brane. Firstly we consider a five-dimensional gravity model with a Gauss-Bonnet term in the bulk and an induced gravity term on a 2-brane of codimension-2. We show that this system admits BTZ black holes on the 2-brane which are extended into the bulk with regular horizons. Furthermore we discuss black hole solutions in six-dimensional gravity with a Gauss-Bonnet term in the bulk and an induced gravity term on a thin 3-brane of codimension-2. We show that these black holes can be localized on the brane, and they can further be extended into the bulk by a warp function. These solutions have regular horizons and no other curvature singularities appear apart from the string-like ones. The projection of the Gauss-Bonnet term on the brane imposes a constraint relation which requires the presence of matter in the extra dimensions. Additionally we address the stability issue of the five-dimensional solutions. In order to do so, we derive the Lichnerowicz equation in the presence of the Gauss-Bonnet term. Using the modified Lichnerowicz equation we study the metric perturbations of Gauss- Bonnet black strings in codimension-2 braneworlds. Apart from the above analysis, we consider a codimension-1 scenario in a five-dimensional theory, where the extra spatial dimension has different scaling than the other four dimensions. We find background maximally symmetric solutions, when the bulk is filled with a cosmological constant and at the same time it has a three-brane embedded in it. These background solutions are reminiscent of Randall-Sundrum warped metrics, with bulk curvature depending on the parameters of the breaking of diffeomorphism invariance. Subsequently, we consider the scalar perturbation sector of the theory and show that it has certain pathologies and the striking feature that in the limit where the diffeomorphism invariance is restored, there remain ghost scalar mode(s) in the spectrum.