Asymptotic structure of symmetry reduced general relativity

Aug, 1996
38 pages
Published in:
  • Phys.Rev.D 55 (1997) 669-686
e-Print:
Report number:
  • CGPG-96-5-1

Citations per year

199620032010201720240510152025
Abstract: (arXiv)
Gravitational waves with a space-translation Killing field are considered. In this case, the 4-dimensional Einstein vacuum equations are equivalent to the 3-dimensional Einstein equations with certain matter sources. This interplay between 4- and 3- dimensional general relativity can be exploited effectively to analyze issues pertaining to 4 dimensions in terms of the 3-dimensional structures. An example is provided by the asymptotic structure at null infinity: While these space-times fail to be asymptotically flat in 4 dimensions, they can admit a regular completion at null infinity in 3 dimensions. This completion is used to analyze the asymptotic symmetries, introduce the analog of the 4-dimensional Bondi energy-momentum and write down a flux formula. The analysis is also of interest from a purely 3-dimensional perspective because it pertains to a diffeomorphism invariant 3-dimensional field theory with {\it local} degrees of freedom, i.e., to a midi-superspace. Furthermore, due to certain peculiarities of 3 dimensions, the description of null infinity does have a number of features that are quite surprising because they do not arise in the Bondi-Penrose description in 4 dimensions.
Note:
  • 39 Pages, REVTEX, CGPG-96/5-1
  • 04.20.Ha
  • 04.30.Nk
  • 04.60.Kz
  • general relativity
  • gravitational radiation: asymptotic behavior
  • Einstein equation
  • dimension: 4
  • dimension: 3
  • space-time
  • conservation law: energy-momentum