Distorting black hole solutions of the vacuum Einstein equations

The uniqueness theorem in four-dimensional general relativity states that stationary isolated black holes in vacuum spacetime must have spherical horizons, described only by the two-parameter family of Kerr solutions. However, this uniqueness does not apply in dimensions higher than four, allowing various black holes with non-spherical shapes, such as black rings, and spherical black holes with bubbles (non-collapsed two-spheres) in the exterior region. On the other hand, black holes rarely exist in isolation; they interact dynamically with surrounding gravitational fields and external matter sources. Understanding these interactions is essential for comprehending the full range of black hole properties and behaviors. This thesis explores distorted black hole solutions to the vacuum Einstein equations, focusing specifically on fivedimensional scenarios. In chapter 3 of this thesis, a distorted local static vacuum black hole-bubble solution is derived via the superposition principle for the Weyl class of solutions. It is smooth in the interior region and free of conical singularities. The distortion represents the influence of external matter in the asymptotic region, modifying the geometry near the black hole. By carefully choosing the distortion, we showed that conical singularities in the undistorted geometry can be removed. In chapter 4, extending to stationary, non-static settings, the research employs advanced solitonic solution-generating techniques to derive a novel distorted rotating black ring solution. This solution begins with a distorted Minkowski spacetime as a seed solution and evolves through solitonic transformations into a distorted rotating black ring configuration. This solution can allow us to investigate how external gravitational fields affect the horizon structure and singularity. In chapter 5, the thesis analyzes the distorted Myers-Perry black hole with a single angular momentum. It carefully examines how external matter affects the shape and curvature of the black hole's horizon. Through analytical and numerical methods, we find significant changes, emphasizing the importance of external influences in black hole physics.