Current research is focussed on extending our knowledge of how gravity behaves on small scales and near black hole horizons, with various modifications which may probe the low energy limits of quantum gravity. This thesis is concerned with such modifications to gravity and their implications. In chapter two thermodynamical stability analyses are performed on higher dimensional Kerr anti de Sitter black holes. We find conditions for the black holes to be able to be in thermal equilibrium with their surroundings and for the background to be stable against classical tensor perturbations. In chapter three new spherically symmetric gravastar solutions, stable to radial perturbations, are found by utilising the construction of Visser and Wiltshire. The solutions possess an anti de Sitter or de Sitter interior and a Schwarzschild (anti) de Sitter or Reissner Nordstrom exterior. We find a wide range of parameters which allow stable gravastar solutions, and present the different qualitative behaviors of the equation of state for these parameters. In chapter four a six dimensional warped brane world compactification of the Salam-Sezgin supergravity model is constructed by generalizing an earlier hybrid Kaluza Klein / Randall Sundrum construction. We demonstrate that the model reproduces localized gravity on the brane in the expected form of a Newtonian potential with Yukawa type corrections. We show that allowed parameter ranges include values which potentially solve the hierarchy problem. The class of solutions given applies to Ricci flat geometries in four dimensions, and consequently includes brane world realisations of the Schwarzschild and Kerr black holes as particular examples. Arguments are given which suggest that the hybrid compactification of the Salam Sezgin model can be extended to reductions to arbitrary Einstein space geometries in four dimensions. This work furthers our understanding of higher dimensional general relativity, which is potentially interesting given the possibility that higher dimensions may become observable at the TeV scale, which will be probed in the Large Hadron Collider in the next few years.

Current research is focussed on extending our knowledge of how gravity behaves on small scales and near black hole horizons, with various modifications which may probe the low energy limits of quantum gravity. This thesis is concerned with such modifications to gravity and their implications. In chapter two thermodynamical stability analyses are performed on higher dimensional Kerr anti de Sitter black holes. We find conditions for the black holes to be able to be in thermal equilibrium with their surroundings and for the background to be stable against classical tensor perturbations. In chapter three new spherically symmetric gravastar solutions, stable to radial perturbations, are found by utilising the construction of Visser and Wiltshire. The solutions possess an anti de Sitter or de Sitter interior and a Schwarzschild (anti) de Sitter or Reissner Nordstrom exterior. We find a wide range of parameters which allow stable gravastar solutions, and present the different qualitative behaviors of the equation of state for these parameters. In chapter four a six dimensional warped brane world compactification of the Salam-Sezgin supergravity model is constructed by generalizing an earlier hybrid Kaluza Klein / Randall Sundrum construction. We demonstrate that the model reproduces localized gravity on the brane in the expected form of a Newtonian potential with Yukawa type corrections. We show that allowed parameter ranges include values which potentially solve the hierarchy problem. The class of solutions given applies to Ricci flat geometries in four dimensions, and consequently includes brane world realisations of the Schwarzschild and Kerr black holes as particular examples. Arguments are given which suggest that the hybrid compactification of the Salam Sezgin model can be extended to reductions to arbitrary Einstein space geometries in four dimensions. This work furthers our understanding of higher dimensional general relativity, which is potentially interesting given the possibility that higher dimensions may become observable at the TeV scale, which will be probed in the Large Hadron Collider in the next few years.

Dans une première partie de cette thèse, nous donnons des minorations universelles ne dépendant que de la dimension – explicites, de trois invariants globaux des quotients des espaces hyperboliques quaternioniques : leur rayon maximal, leur volume, ainsi que leur caractéristique d’Euler. Nous donnons également une majoration de leur constante de Margulis, montrant que celle-ci décroit au moins comme une puissance négative de la dimension. Dans une seconde partie, nous étudions un réseau remarquable des isométries du plan hyperbolique quaternionique, le groupe modulaire d’Hurwitz. Nous montrons en particulier qu’il est engendré par quatres éléments, et construisons un domaine fondamental pour le sous-groupe des isométries de ce réseau qui stabilisent un point à l’infini. / In the first part of this thesis, we derive explicit universal – that is, depending only on the dimension – lower bounds on three global invariants of quaternionic hyperbolic sapces : their maximal radius, their volume, and their Euler caracteristic. We also exhibit an upper bound on their Margulis constant, showing that this last quantity decreases at least like a negative power of the dimension. In the second part, we study a specific lattice of isometries of the quaternionic hyperbolic plane : the Hurwitz modular group. In particular, we show that this group is generated by four elements, and we construct a fundamental domain for the subgroup of isometries of this lattice stabilising a point on the boundary of the quaternionic hyperbolic plane.

This thesis deals with the creation of the intro with limited size. This work describes methods for reducing the size of the final application. The main part describes methods for generating graphic content and methods for its animation. It deals with creation of textures and geometry. Another part is aimed on the physical simulation of particle and elastic systems.