Super-Geometrodynamics in Higher Dimensions

TL;DR

This paper extends the study of geometrodynamics to higher-dimensional theories, constructing initial data solutions for black holes and wormholes in supergravity and string theory contexts.

Contribution

It provides a systematic method for solving initial value constraints in higher-dimensional theories, including supergravities and string/M-theory limits.

Findings

Constructed initial data for multiple black holes in higher dimensions.

Generated wormhole solutions in higher-dimensional spacetimes.

Extended geometrodynamics framework beyond four dimensions.

Abstract

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.