Abstract
A review of our results on the asymptotic structure of gravity at spatial infinity in four spacetime dimensions is given. Finiteness of the action and integrability of the asymptotic Lorentz boost generators are key criteria that we implement through appropriate boundary conditions. These conditions are “twisted parity conditions,” expressing that the leading order of the asymptotic fields obeys strict parity conditions under the sphere antipodal map up to an improper gauge transformation. The asymptotic symmetries are shown to form the infinite-dimensional Bondi-Metzner-Sachs group, which has a nontrivial action. The charges and their algebra are worked out. The presentation aims at being self-contained and at possessing a pedagogical component.
Highlights
This paper is dedicated to Andrei Alekseevich Slavnov, colleague and friend, on the occasion of his 80th birthday
We have provided in [18, 20] two different sets of boundary conditions for gravity at spatial infinity that are invariant under the BMS group and that yield a well-defined and nontrivial canonical action of that group
One finds that the odd W ’s and even T ’s combine to yield the arbitrary function of the angles parametrizing supertranslations in the null infinity parametrization. This enables one to conclude that the symmetry at spatial infinity is the same BMS4 as the BMS4 uncovered at null infinity
Summary
This paper is dedicated to Andrei Alekseevich Slavnov, colleague and friend, on the occasion of his 80th birthday. Our analysis investigates the asymptotic dynamics of the fields on spacelike hypersurfaces that approach spacelike (Cauchy) hyperplanes at infinity It uses the Hamiltonian formalism of general relativity [12, 1] as its main tool and finds its roots in the pioneering paper [25]. We have provided in [18, 20] two different sets of boundary conditions for gravity at spatial infinity that are invariant under the BMS group and that yield a well-defined and nontrivial canonical action of that group. They must be retained in the asymptotic form of the fields and it would be incorrect to set them to zero This conceptually simple and perhaps even obvious extension of the work [25] (“parity conditions involving a twist given by improper diffeomorphisms”) completely reconciles the symmetry analyses at spatial and null infinity. It is the purpose of this article to systematically review the results of [20] in a self-contained manner, with a somewhat pedagogical emphasis that sheds new light on some features of the derivation
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
