Aspectos clássicos de gravitação topológica e dimensões extras - Tahim, Makarius Oliveira (2008)
In this thesis we study some aspects related with Gravity Theories. Essentially there are two main pieces in this work: (1) mechanisms of eld localization on membranes and (2) a new interpretation for the gravity theory. Related to the eld localization mechanisms two subjects are discussed: the construction of topological gravity models in the context of membranes and localization of tensorial gauge elds in thin membranes (the so called Kalb-Ramond eld). In the rst of these subjects, the important question is try to obtain results compared to those coming from the Randall-Sundrum models, i.e., the solution to the hierarchy problem and the localization of the gravitational eld in the membrane. Nevertheless, the way chosen is related to topological gravity, such models where the space-time metric is not the fundamental entity. There is in the academy a way of thinking which basis is a quantization formalism for gravity. Such searches need the viewpoint in which gravity can be described by constrained topological eld theories. Therefore, to ask about the results of the Randall-Sundrum model in the context of topological gravity may be useful as a test for strictly quantum theory results. In this sense, we make rstly a classical analysis of the possible models, discussing several aspects (symmetry breaking, gauge symmetries, etc.). Firstly we show that in fact we can obtain, in the lines cited above, equations very similar to the Randall-Sundrum results to explain the hierarchy between the masses of the Higgs bosons. Nevertheless, an detailed analysis of how to describe gravity in D = 5 is not made. In this line of reasoning, we construct several models with the same mathematical form of the models of topological gravity (equivalent models), trying to do "localization"over the membranes in order to link this result to the rst cited above. Lastly, we construct e ectively topological gravity on a membrane, regarding the constraints in the space-time orthogonal to the membrane. In the second subject, we study scalar eld models that support kink-like defects emiv bedded in a D = 5 space-time. Such models can be utilized to simulate thin membranes. In this case we analyze the localization of tensor gauge elds, mainly the Kalb-Ramond eld, in the background of several non-singular geometries, unlike those presented in the original Randall-Sundrum model. The result is that the zero-mode for the Kalb-Ramond eld can be localized only in the special background where the dilaton plays an important rule. The second part of this thesis is a little bit speculative. It is about a di erent interpretation of gravitation. The idea is to compare the own space-time to a physical deformable solid. In this sense, we look for the microscopic components of this solid, just like the real crystalline solids which are made of a network containing a myriad of atoms and molecules. For such, we make use of the Landau-Raychaudhuri equation, which is crucial in this discussion. It is discussed a set of tree signs pointing to this idea: (1) the deformation of the space-time volume, (2) the elastic origin of the Einstein-Hilbert action and (3) the relation between Hooke's law and the Einstein's equation for gravitation. An important idea is that the Einstein's equation seems to "emerge"quite naturally in this context.