Comparing General Relativity with Shape Dynamics

Abstract

The aim of this thesis is to compare the strengths and weaknesses of the theories shape dynamics and general relativity using two well-known situations involving spherically symmetric gravitational fields; the pure vacuum solution and the gravitational collapse of a thin shell. Using the formal equivalence between the field equations in a particular spacetime foliation of general relativity we have succeeded in finding relevant solutions that permit a shape dynamics description. We subsequently provide an interpretation of these solutions in terms of the principles of shape dynamics. Although the two theories are locally equivalent at the level of the field equations, global or topological differences may yet arise in the classical theory, furthermore, the fact that the theories contain different local symmetries and corresponding constraint algebras may lead to different predictions after quantization.