1305.0310 (Henrique Gomes)

A Birkhoff theorem for Shape Dynamics    [PDF]

Henrique Gomes

Here we use the equations of motion of Shape Dynamics in its asymptotically flat version to derive a Birkhoff theorem. There are three significant differences with respect to the usual Birkhoff theorem in GR. The first regards the posing of the problem: in Shape Dynamics we must establish from the start the boundary conditions of our phase space variables. Thus unlike the GR Birkhoff theorem, which yields a static 4-metric from vacuum and spherical symmetry irrespectively of the boundary conditions, we have to postulate asymptotically flat boundary conditions from the start. The second difference regards the construction of the solution: we heavily use the Shape Dynamics spatial Weyl gauge freedom to simplify the problem. The remaining difference is that the solution obtained is uniquely the isotropic wormhole solution, in which no singularity is present, as opposed to maximally extended Schwarzschild.

View original: http://arxiv.org/abs/1305.0310