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Supermassive black hole binaries (SMBHBs) are among the most powerful known sources of gravitational waves (GWs). Accordingly, these systems could dominate the stochastic gravitational wave background (GWB) in the micro- and millihertz frequency range. The time until the merger of two SMBHs in the nucleus of a galaxy can be shortened through dynamical friction due to the presence of dark matter (DM) spikes around the SMBHs. To calculate the orbital evolution of individual SMBHBs within the Newtonian approximation, the SMBHBpy code is developed. This work confirms that the GW signals from SMBHBs with DM spikes can be clearly distinguished from those without any matter. Making use of the upper limit on the characteristic strain of the GWB derived from the data of the Cassini spacecraft mission in 2001/2002, a lower limit on the matter density around SMBHBs is derived in this study. The result is subsequently compared with the theoretical density profiles for cold dark matter and self-interacting dark matter spikes.
As part of the research for this thesis, a momentum spectrometer was set up and initial measurements on accelerated ions were performed. For this purpose, the necessary hardware for the operation of the spectrometer and for high-precision measurements was were assembled. A control system for remote operation was developed and the spectrometer was installed at the used beamline.
There, measurements of low-energy ion beams in superposition with electrons confined in a Gabor lens can be carried out.
Investigations were made on both the Gabor lens-generated ions and the beam ions, leading to first results regarding the charge changes of beam ions during propagation through an electron atmosphere.
The Generalized Uncertainty Principle (GUP) arises from Quantum Gravity thought experiments and contains a minimal lenght. In this thesis I calculate Schwarzschild Black Holes that are modified by the GUP. These Black Holes have the property, that their temperature does not diverge for small masses, although they still posses a curvature singularity. I calculate analytically that in more than 3+1 dimensions the temperature diverges again.