Asymptotic structure of symmetry-reduced general relativity

Article

Asymptotic structure of symmetry-reduced general relativity

Ashtekar, A.; Bičák, J.; Schmidt, B.~G.

Phys. Rev. D 55(0), 669-686 (1997)

Abstract

Gravitational waves with a space-translation Killing field are considered. Because of the symmetry, the four-dimensional Einstein vacuum equations are equivalent to the three-dimensional Einstein equations with certain matter sources. This interplay between four- and three-dimensional general relativity can be exploited effectively to analyze issues pertaining to four dimensions in terms of the three-dimensional structures. An example is provided by the asymptotic structure at null infinity: While these space-times fail to be asymptotically flat in four dimensions, they can admit a regular completion at null infinity in three dimensions. This completion is used to analyze the asymptotic symmetries, introduce the analogue of the four-dimensional Bondi energy momentum, and write down a flux formula. The analysis is also of interest from a purely three-dimensional perspective because it pertains to a diffeomorphism-invariant three-dimensional field theory with local degrees of freedom, i.e., to a midisuperspace. Furthermore, because of certain peculiarities of three dimensions, the description of null infinity has a number of features that are quite surprising because they do not arise in the Bondi-Penrose description in four dimensions.

Institute authors

Bičák, Jiří

Supported by

GACR 202/96/0206 — Relativistic physics and astrophysics
GAUK 230/1996 — Relativistická teorie gravitace, astrofyzika a kosmologie

BibTeX

@article{UTF274,
  author        = {Ashtekar, A. and Bičák, J. and Schmidt, B.\textasciitilde{}G.},
  title         = {{Asymptotic structure of symmetry-reduced general relativity}},
  journal       = {Phys. Rev. D},
  volume        = {55},
  number        = {0},
  pages         = {669-686},
  year          = {1997},
  doi           = {10.1103/PhysRevD.55.669},
  eprint        = {gr-qc/9608042},
  archivePrefix = {arXiv},
  url           = {http://link.aps.org/abstract/PRD/v55/p669},
}