On 29.07.2021, the "Award of the Friends of the University of Stuttgart" was conferred for the 48th time. It was endowed on the occasion of the 50th anniversary of the Association of Friends of the University of Stuttgart in 1973. The "Award of the Friends of the University of Stuttgart" honors outstanding scientific achievements and is also intended to promote contact between the friends of the University of Stuttgart and the students. Mr. Paul Schwahn (IGT) received the prize for his master thesis on "Einstein deformations on homogeneous spaces" (supervisor Prof. Uwe Semmelmann).
Abstract:
Einstein metrics on Riemannian manifolds naturally arise in General Relativity as solutions of the Einstein field equations in a vacuum with cosmological constant. This already gives them quite a bit of relevance in physics. We are interested in how one could smoothly vary an Einstein metric while still retaining the Einstein property, i.e. how to deform the Einstein metric through a curve of Einstein metrics. If one considers the problem on an infinitesimal scale, what are the constraints on the direction in which our deformation might go? It turns out that the space of such infinitesimal deformations can be described as an eigenspace of a particular operator. This operator also has a physical relevance; for example, it is present in higher-dimensional gravity theories, where the stability of black holes is analyzed. In total, this should be a sufficient justification to study Einstein manifolds and their deformations, if one is not already convinced by the fact that problems in Riemannian geometry are interesting in themselves.