Equilibrium configurations of two charged masses in General Relativity

An asymptotically flat static solution of Einstein-Maxwell equations which describes the field of two non-extreme Reissner - Nordstr\"om sources in equilibrium is presented. It is expressed in terms of physical parameters of the sources (their masses, charges and separating distance). Very simple analytical forms were found for the solution as well as for the equilibrium condition which guarantees the absence of any struts on the symmetry axis. This condition shows that the equilibrium is not possible for two black holes or for two naked singularities. However, in the case when one of the sources is a black hole and another one is a naked singularity, the equilibrium is possible at some distance separating the sources. It is interesting that for appropriately chosen parameters even a Schwarzschild black hole together with a naked singularity can be "suspended" freely in the superposition of their fields.Comment: 4 pages; accepted for publication in Phys. Rev.

Design and analysis of a quasi-optical beam combiner for the QUBIC CMB interferometer

In winter 2009 a number of physicists met in Paris to discuss the prospect of observing the CMB B-mode polarization using a novel technique called bolometric interferometry. This was the first meeting of what would later become the QUBIC collaboration. In this thesis we discuss the scientific reasons for CMB observation, we present a detailed explanation of how QUBIC will use bolometric interferometry to measure CMB polarization and in particular we discuss the author's contribution to the project. As part of the sub-mm optics research group in the National University of Ireland Maynooth the author was charged with the design and modeling of the optics that would focus the beam from the sky onto the bolometric detectors. This thesis describes various types of re ecting and refracting optics that were investigated. The results we present are useful not only for the QUBIC instrument, but for the design of imaging experiments in general. Detection of CMB B-mode polarization is one of the supreme goals of modern cosmology. The faintness of this signal, combined with the interferometric observing technique, places extreme performance specifications on the QUBIC optics. Fortunately, as we shall show, there are types of well-known re ecting and refracting telescopes that are suitable for QUBIC. In this thesis I propose a design for the quasi-optical combiner that will perform as required