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On the relation between the Einstein field equations and the Jacobi–Ricci–Bianchi system

Norbert Van den Bergh UGent (2013) CLASSICAL AND QUANTUM GRAVITY. 30(14).
abstract
The 1 + 3 covariant equations, embedded in an extended tetrad formalism and describing a spacetime with an arbitrary energy–momentum distribution, are reconsidered. It is shown that, provided the 1 + 3 splitting is performed with respect to a generic time-like congruence with a tangent vector u, the Einstein field equations can be regarded as the integrability conditions for the Jacobi and Bianchi equations together with the Ricci equations for u. The same conclusion holds for a generic null congruence in the Newman–Penrose framework.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
GENERAL-RELATIVITY, GRAVITY, NEWMAN-PENROSE FORMALISM, UNIVERSES, VARIABLES, COVARIANT, WAVES
journal title
CLASSICAL AND QUANTUM GRAVITY
Class. Quantum Grav.
volume
30
issue
14
pages
14 pages
publisher
Institute of Physics
Web of Science type
Article
Web of Science id
000321620300011
JCR category
PHYSICS, MULTIDISCIPLINARY
JCR impact factor
3.103 (2013)
JCR rank
13/78 (2013)
JCR quartile
1 (2013)
ISSN
0264-9381
DOI
10.1088/0264-9381/30/14/145010
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
3260562
handle
http://hdl.handle.net/1854/LU-3260562
date created
2013-06-18 12:15:51
date last changed
2016-12-19 15:45:01
@article{3260562,
  abstract     = {The 1 + 3 covariant equations, embedded in an extended tetrad formalism and describing a spacetime with an arbitrary energy--momentum distribution, are reconsidered. It is shown that, provided the 1 + 3 splitting is performed with respect to a generic time-like congruence with a tangent vector u, the Einstein field equations can be regarded as the integrability conditions for the Jacobi and Bianchi equations together with the Ricci equations for u. The same conclusion holds for a generic null congruence in the Newman--Penrose framework.},
  author       = {Van den Bergh, Norbert},
  issn         = {0264-9381},
  journal      = {CLASSICAL AND QUANTUM GRAVITY},
  keyword      = {GENERAL-RELATIVITY,GRAVITY,NEWMAN-PENROSE FORMALISM,UNIVERSES,VARIABLES,COVARIANT,WAVES},
  language     = {eng},
  number       = {14},
  pages        = {14},
  publisher    = {Institute of Physics},
  title        = {On the relation between the Einstein field equations and the Jacobi--Ricci--Bianchi system},
  url          = {http://dx.doi.org/10.1088/0264-9381/30/14/145010},
  volume       = {30},
  year         = {2013},
}

Chicago
Van den Bergh, Norbert. 2013. “On the Relation Between the Einstein Field Equations and the Jacobi–Ricci–Bianchi System.” Classical and Quantum Gravity 30 (14).
APA
Van den Bergh, N. (2013). On the relation between the Einstein field equations and the Jacobi–Ricci–Bianchi system. CLASSICAL AND QUANTUM GRAVITY, 30(14).
Vancouver
1.
Van den Bergh N. On the relation between the Einstein field equations and the Jacobi–Ricci–Bianchi system. CLASSICAL AND QUANTUM GRAVITY. Institute of Physics; 2013;30(14).
MLA
Van den Bergh, Norbert. “On the Relation Between the Einstein Field Equations and the Jacobi–Ricci–Bianchi System.” CLASSICAL AND QUANTUM GRAVITY 30.14 (2013): n. pag. Print.