Polarização de vácuo e correntes induzidas por uma corda cósmica no espaço-tempo anti-de Sitter

Abstract

In this thesis, we investigate the combined effects of the spacetime curvature, the nontrivial topology and the presence of external fields on the quantum vacuum fluctuations associated with bosonic and fermionic charged fields. We analyze the bosonic current densities induced by a magnetic flux along the core of an idealized cosmic string in a anti-de Sitter space-time with (D + 1) dimensions, assuming that an extra dimension is compactified and the presence of a magnetic flux enclosed by the compactified axis. In this context, we show, for instance, that only azimuthal and axial current densities are induced. The vacuum expectation values of the squared field and the energy-momentum tensor associated with the bosonic field are also analyzed. To develop these calculations, the complete set of normalized wave functions obeying a quasiperiodicity condition along the extra dimension was obtained and the positive frequency Wightman function has been constructed. The vacuum expectation values of the current densities, fermionic condensate and energy-momentum tensor generated in the vacuum of a fermionic field were also analyzed. In this case, the geometry considered was the (4 + 1)−dimensional anti-de Sitter space-time in the presence of a magnetic flux along the axis of a cosmic string and a compact extra dimension with a magnetic flux enclosed by its compactified axis. To obtain the vacuum expectation values mentioned above, the Dirac equation in curved space-time for this geometry was solved and the fermionic modes were obtained. Finally, in the last chapter of this thesis we analyze the fermionic current densities induced by a magnetic flux along a cosmic string and a brane in the geometry of the anti-de Sitter space-time in (4 + 1) dimensions. In this case, the brane is parallel to the anti-de Sitter boundary and the cosmic string is orthogonal to the brane. The brane divides the spacetime into two regions with different vacuum properties, and the only induced component along the azimuthal direction is studied in each of these regions. In all investigations performed, analyzes of special, asymptotic and numerical cases were made for the results obtained.