1212.1755 (Henrique Gomes)

Poincaré invariance and asymptotic flatness in Shape Dynamics    [PDF]

Henrique Gomes

Shape Dynamics is a theory of gravity that sheds refoliation invariance in favor of spatial Weyl invariance. It is a canonical theory, constructed from a Hamiltonian, 3+1 perspective. One of the main deficits of Shape Dynamics is that its Hamiltonian is only implicitly constructed as a functional of the phase space variables. In this paper we aim to achieve a new perspective on tackling this problem. For this, we write down the equations of motion for Shape Dynamics. Although there is still an implicit function in these equations of motion, we can make it explicit for particular solutions. In particular, we construct Shape Dynamics over a curve in phase space representing a Minkowski spacetime, and use this to show that in this case Shape Dynamics possesses Poincar\'e symmetry for appropriate boundary conditions. The proper treatment of such boundary conditions leads us to completely formulate Shape Dynamics for open manifolds in the asymptotically flat case. We study the charges arising for Shape Dynamics in flat asymptotic boundary conditions and find a new component for the energy charge. This new charge, when added to the usual ADM energy to make up the total energy for Shape Dynamics, is completely Weyl invariant. We then use the equations of motion once again to find a non-trivial solution of Shape Dynamics, consisting of a flat static Universe with a point-like mass at the center. We calculate its energy and rederive the usual Schwarzschild mass.

View original: http://arxiv.org/abs/1212.1755