Alguns resultados acerca de campos escalares em buracos negros, cosmologia quântica e flutuações quânticas da geometria

Abstract

We consider charged massive scalar fields in the gravitational and electromagnetic fields produced by different kinds of black holes, namely, the ones with and without a cosmic string, surrounded by a magnetic field, and in the f(R) theory of gravity. The special cases of massless and uncharged particles are also examined. Exact solutions of both angular and radial parts of the covariant Klein-Gordon equation in these backgrounds are obtained in terms of the Heun functions. From the radial solutions, we obtain the exact wave solutions near the event horizons of the black holes and discuss the Hawking radiation spectrum. We apply the Heun functions properties to study the resonant frequencies (quasispectrum) and the scattering process of scalar waves, in a class of spacetimes. In the analogue gravity approach, namely, the spacetime of both three dimensional rotating and four dimensional canonical acoustic black holes, we obtain the analytic solutions of the radial part of the massless Klein-Gordon equation. From these solutions, we obtain the scalar wavesneartheacousticeventhorizonanddiscusstheanalogueHawkingradiation.In the quantum Newtonian cosmology, we obtain the exact solution of the Schrödinger equationforaparticle(galaxy)movinginthisuniverse.Thewavefunctionsaregiven in terms of the Heun functions, and the energy levels depend on the cosmological constant. The solutions of the Wheeler-DeWitt equation in a homogeneous and isotropic universe are also obtained and given in terms of the Heun functions for the spatially closed, flat, and open geometries of the Friedmann-Robertson-Walker universe filled with different forms of energy. We discuss the quantum fluctuations of the geodesic deviation equation in Minkowski spacetime for three different sources of the Riemann tensor fluctuations, namely, thermal bath of gravitons, gravitons in a squeezed state, and graviton vacuum state.