Shape dynamics is a 3D conformally invariant theory of gravity that possesses a large set of solutions in common with general relativity. When looked at closely, these solutions are found to behave in surprising ways; in order to probe the fitness of shape dynamics as a viable alternative to General Relativity one must find and understand increasingly more-complex, less-symmetrical exact solutions on which to base perturbative studies and numerical analyses to compare them with data. Spherically symmetric exact solutions have been studied, but only in a static vacuum setup. In this work we construct a class of time-dependent exact solutions of Shape Dynamics from first principles, representing a central inhomogeneity in an evolving cosmological environment. By assuming only a perfect fluid source in a spherically symmetric geometry, we show that this fully dynamic nonvacuum solution satisfies in all generality the Hamiltonian structure of shape dynamics. The simplest choice of solutions is shown to be a member of the McVittie family.

• Received 21 June 2016

DOI:https://doi.org/10.1103/PhysRevD.94.064023