Nonlinear perturbations of Reissner-Nordström black holes
We develop a nonlinear perturbation theory of Reissner-Nordstr\"om black holes. We show that, at each perturbation level, Einstein-Maxwell equations can be reduced to four inhomogeneous wave equations, two for polar and two for axial sector. Gravitational part of these equations is similar to Regge-Wheeler and Zerilli equations with source and additional coupling to the electromagnetic sector. We construct solutions to the inhomogeneous part of wave equations in terms of sources for Einstein-Maxwell equations. We discuss $\ell=0$ and $ \ell=1$ cases separately.
Towards a theory of nonlinear gravitational waves: A systematic approach to nonlinear gravitational perturbations in the vacuum
We present a systematic and robust approach to nonlinear gravitational perturbations of vacuum spacetimes. This approach provides a basis for a theory of nonlinear gravitational waves. In particular, we show that the system of perturbative Einstein equations reduces at each perturbation order to two (for each gravitational mode in 3 + 1 dimensions on which our study is focused) scalar wave equations, and then we show how the metric perturbations can be explicitly obtained, once the solutions to these scalar wave equations are known. These results show that the concept of polarization of a gravitational wave does make sense also beyond the linear approximation.
Investigation of scatter radiation of non-circular X-ray scan trajectories
Modern interventional X-ray devices are highly maneuverable and allow complex 3D imaging trajectories. New scan trajectories enable not only optimized object sampling but also introduce new approaches for dynamic 3D imaging. In this paper, we investigated the scatter radiation of two different scan trajectories. The scatter radiation was sampled by a rail setup with dosimeters at defined positions. After data analysis, contour maps were generated which show for four exemplary heights the scatter radiation distribution. The alternative scan trajectory showed smaller dose exposures at heights correlated to upper torso and head areas of a model physician. Keywords—Image acquisition, alternative scan trajectory, circular tomosynthesis, scatter radiation distribution