Super-Geometrodynamics in Higher Dimensions

The geometrodynamics of the four-dimensional Einstein and Einstein-Maxwell theories were first studied by Wheeler and Misner more than fifty years ago, by constructing solutions of the constraints on an initial spatial slice in a Hamiltonian formulation of the theories. More recently these considerations were extended to various four-dimensional theories with additional fields, encompassing cases that arise in supergravity and the low-energy limit of compactified string theory. In this paper we extend these considerations further, by constructing solutions of the initial value constraints in higher spacetime dimensions, for wide classes of theories that include supergravities and the low-energy limits of string and M-theory. We obtain time-symmetric initial data sets for multiple black hole spacetimes and also wormholes in higher dimensions.