Ott Vilson will defend his PhD thesis "Transformation properties and invariants in scalar-tensor theories of gravity" (physics) on 20 March 2019.
Dr. Piret Kuusk, Institute of Physics, University of Tartu
Dr. Sergei Vernov, Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Russia
Dr. Luca Marzola, National Institute of Chemical Physics and Biophysics, Tallinn, Estonia
Einstein’s general relativity, current standard theory of gravity is a tensor theory. Its central object is the metric tensor, i.e., the prescription for calculating the length of line segments and angles between two of them. The term ‘tensor’ emphasizes that the prescription, pictured as a box with input and output, takes exactly two of those line segments (or twice the same in case of length) and produces one number which is the same for different observers. The key idea behind Einstein’s theory is to consider the situation where in addition to extrinsic information, i.e., the properties of the line segments, the output depends also on the intrinsic information of the prescription. It is the latter, the intrinsic information of the prescription for calculating lengths and angles that is dynamical and spacetime-point-dependent in general relativity, thus permitting to describe different curved spacetime geometries. In scalar-tensor theories of gravity Einstein’s theory is extended by adding a scalar, a sibling of a tensor that receives no line segments and thus produces an observer-independent number solely based on spacetime-point-dependent intrinsic information. In the thesis I study transformations that mix the intrinsic information of the metric tensor and the scalar in a manner that preserves the causal structure. In particular I consider how different expressions change under the transformations, and identify those which remain unchanged, i.e., the so-called invariants. The latter are used to clarify relations between different formulations of the same family of theories on different levels of abstraction. I conclude that the most convenient level for studying the transformation properties under such transformations is the most abstract one as in that case each expression has an explicit and unique transformation rule.