The BMS group and generalized gravitational instantons

Abstract

The ordinary Bondi–Metzner–Sachs (BMS) group B is the best candidate for the fundamental symmetry group of General Relativity. It has been shown that B admits generalizations to real space–times of any signature, and also to complex space–times. It has been suggested that certain continuous unitary irreducible representations (IRs) of B and of its generalizations correspond to gravitational instantons. Here I make this correspondence more precise and I take this suggestion one step further by arguing that a subclass of IRs of B and of its generalizations correspond to generalized gravitational instantons. Some of these generalized gravitational instantons involve in their definition certain subgroups of the Cartesian product group Cn×Cm, where Cr is the cyclic group of order r. With this motivation, I give the subgroups of Cn×Cm explicitly.