A unified treatment of null and spatial infinity in general relativity. I. Universal structure, asymptotic symmetries, and conserved quantities at spatial infinity

1978 ◽  
Vol 19 (7) ◽  
pp. 1542-1566 ◽  
Author(s):  
Abhay Ashtekar ◽  
R. O. Hansen
Keyword(s):  
General Relativity ◽  
Conserved Quantities ◽  
Spatial Infinity ◽  
Universal Structure ◽  
Asymptotic Symmetries

Twistor theory and the energy—momentum and angular momentum of the gravitational field at spatial infinity

1983 ◽  
Vol 390 (1798) ◽  
pp. 191-215 ◽  
Keyword(s):  
General Relativity ◽  
Angular Momentum ◽  
Twistor Space ◽  
Conserved Quantities ◽  
Twistor Theory ◽  
Coordinate Transformations ◽  
Spatial Infinity ◽  
Weyl Curvature ◽  
Linearized Theory ◽  
Math Phys

Penrose’s ‘quasi-local mass and angular momentum’ (Penrose, Proc. R. Soc. Lond . A 381, 53 (1982)) is investigated for 2-surfaces near spatial infinity in both linearized theory on Minkowski space and full general relativity. It is shown that for space-times that are radially smooth of order one in the sense of Beig & Schmidt ( Communs math. Phys . 87, 65 (1982)), with asymptotically electric Weyl curvature, there exists a global concept of a twistor space at spatial infinity. Global conservation laws for the energy—momentum and angular momentum are obtained, and the ten conserved quantities are shown to be invariant under asymptotic coordinate transformations. The relation to other definitions is discussed briefly.

Kleinian characterization of asymptotic symmetries of real general relativity

1993 ◽  
Vol 441 (1913) ◽  
pp. 465-471 ◽  
Keyword(s):  
General Relativity ◽  
Automorphism Group ◽  
Group Action ◽  
Radon Transform ◽  
Symmetry Groups ◽  
Asymptotic Symmetry ◽  
The Real ◽  
The Given ◽  
Asymptotic Symmetries

According to Klein’s Erlanger programme, one may (indirectly) specify a geometry by giving a group action. Conversely, given a group action, one may ask for the corresponding geometry. Recently, I showed that the real asymptotic symmetry groups of general relativity (in any signature) have natural ‘projective’ classical actions on suitable ‘Radon transform’ spaces of affine 3-planes in flat 4-space. In this paper, I give concrete models for these groups and actions. Also, for the ‘atomic’ cases, I give geometric structures for the spaces of affine 3-planes for which the given actions are the automorphism group.

scholarly journals COLLECTIVE AND RELATIVE VARIABLES FOR A CLASSICAL KLEIN–GORDON FIELD

1999 ◽  
Vol 14 (21) ◽  
pp. 3387-3420 ◽  
Author(s):  
G. LONGHI ◽  
M. MATERASSI
Keyword(s):  
General Relativity ◽  
Asymptotic Behavior ◽  
Harmonic Analysis ◽  
Momentum Space ◽  
Conserved Quantities ◽  
Canonical Transformations ◽  
Collective Variables ◽  
Klein Gordon ◽  
Definition Of

In this paper a set of canonical collective variables is defined for a classical Klein–Gordon field and the problem of the definition of a set of canonical relative variables is discussed. This last point is approached by means of a harmonic analysis in momentum space. This analysis shows that the relative variables can be defined if certain conditions are fulfilled by the field configurations. These conditions are expressed by the vanishing of a set of conserved quantities, referred to as supertranslations since as canonical observables they generate a set of canonical transformations whose algebra is the same as that which arises in the study of the asymptotic behavior of the metric of an isolated system in General Relativity.9

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