Asymptotically Flat Initial Data for Gravitational Wave Spacetimes, Conformal Compactification and Conformal Symmetry
نویسنده
چکیده
We study the utilization of conformal compactification within the conformal approach to solving the constraints of general relativity for asymptotically flat initial data. After a general discussion of the framework, particular attention is paid to simplifications that arise when restricting to a class of initial data which have a certain U(1)×U(1) conformal symmetry.
منابع مشابه
Conformal compactification and cycle-preserving symmetries of spacetimes
The cycle-preserving symmetries for the nine two-dimensional real spaces of constant curvature are collectively obtained within a Cayley–Klein framework. This approach affords a unified and global study of the conformal structure of the three classical Riemannian spaces as well as of the six relativistic and non-relativistic spacetimes (Minkowskian, de Sitter, anti-de Sitter, both Newton–Hooke ...
متن کاملSymmetries of asymptotically flat four-dimensional spacetimes at null infinity revisited.
It is shown that the symmetry algebra of asymptotically flat spacetimes at null infinity in 4 dimensions should be taken as the semidirect sum of supertranslations with infinitesimal local conformal transformations and not, as usually done, with the Lorentz algebra. As a consequence, two-dimensional conformal field theory techniques will play as fundamental a role in this context of direct phys...
متن کاملSpacetimes admitting quasi-conformal curvature tensor
The object of the present paper is to study spacetimes admitting quasi-conformal curvature tensor. At first we prove that a quasi-conformally flat spacetime is Einstein and hence it is of constant curvature and the energy momentum tensor of such a spacetime satisfying Einstein's field equation with cosmological constant is covariant constant. Next, we prove that if the perfect flui...
متن کاملOn the Relation between Adm and Bondi Energy-momenta Ii – Radiative Spatial Infinity
It is a fundamental problem in gravitational radiation what the relation is between the ADM energy-momentum and the Bondi energy-momentum. Ashtekar and Magnon-Ashtekar demonstrated the mass at spatial infinity is the past limit of the Bondi mass taken as the cut approaches the “point” of spatial infinity in the frame of Penrose conformal compactification [2]. It was proved the standard ADM mass...
متن کاملar X iv : g r - qc / 0 40 80 62 v 1 1 8 A ug 2 00 4 Time asymmetric spacetimes near null and spatial infinity . I . Expansions of developments of conformally flat data
The Conformal Einstein equations and the representation of spatial infinity as a cylinder introduced by Friedrich are used to analyse the behaviour of the gravitational field near null and spatial infinity for the development of data which are asymptotically Euclidean, conformally flat and time asymmetric. Our analysis allows for initial data whose second fundamental form is more general than t...
متن کامل