Spinores sob a ação da gravidade e tachyons no espaço-tempo quadridimensional

Orientador: Jair LucindaDissertação (Mestrado) - Universidade Federal do ParanaResumo: Neste trabalho, analisamos a formulação da gravidade dentro do contexto de "Field-Boost" e suas conseqüências dinâmicas. Obtemos as equações de Klein-Gordon e de Dirac, modificadas pela ação do campo gravitacional. Através das propriedades de transformação de spinores sob o grupo de Lorentz estendido deduzimos a equação de Dirac obtida anteriormente por outros processos. Estudamos os referenciais super-luminais e sua correspondência, através das transformações de "Field-Boost", com referenciais subluminais, como conseqüência dessa análise chegamos a conclusão de que táquions são produzidos no interior de buracos negros. Finalmente obtemos algumas soluções simples da equação de Dirac.Abstract: In this dissertation, we analyzed the gravity formulation in the context of "Field- Boost" and its dynamical aftermath. We obtained the Klein-Gordon and Dirac modified equations by the action of the gravitational field. From the properties of spinors transformation of the Lorentz extended group we derived the Dirac equation obtained previously by other processes. We studied the super-luminal frames and its correspondence, through the "Field-Boost" transformations, with sub-luminal frames, as a consequence of this analysis we found out that tachyons are produced inside the black holes. Finally, we obtained some simple solutions of the Dirac equations

Tachyonization of the \LaCDM cosmological model

In this work a tachyonization of the $\Lambda$CDM model for a spatially flat Friedmann-Robertson-Walker space-time is proposed. A tachyon field and a cosmological constant are considered as the sources of the gravitational field. Starting from a stability analysis and from the exact solutions for a standard tachyon field driven by a given potential, the search for a large set of cosmological models which contain the $\Lambda$CDM model is investigated. By the use of internal transformations two new kinds of tachyon fields are derived from the standard tachyon field, namely, a complementary and a phantom tachyon fields. Numerical solutions for the three kinds of tachyon fields are determined and it is shown that the standard and complementary tachyon fields reproduces the $\Lambda$CDM model as a limiting case. The standard tachyon field can also describe a transition from an accelerated to a decelerated regime, behaving as an inflaton field at early times and as a matter field at late times. The complementary tachyon field always behaves as a matter field. The phantom tachyon field is characterized by a rapid expansion where its energy density increases with time.Comment: Version accepted for publication in GR