TY - JOUR
T1 - Exact solutions admitting isometry groups Gr ⫆ abelian G3
AU - Ziad, M.
N1 - Funding Information:
I am highly thankful to MAH MacCallum for his useful comments on some of the work done here. A part of this work was presented in 21st International Conference on General Relativity and Gravitation, Columbia University, New York. Travel grant by Sultan Qaboos University, Sultanate of Oman, to present this work in GR21 is gratefully acknowledged.
Publisher Copyright:
© 2018 The Author(s). Published by IOP Publishing Ltd.
PY - 2018/11
Y1 - 2018/11
N2 - Metrics admitting a minimal three dimensional Abelian isometry group, G3 are classified according to their Petrov types and metrics, giving all type O and D metrics explicitly, without imposing a source condition. The corresponding maximal Lie algebras for these metrics are obtained and identified as well. The type O metrics admit a maximal Gr (Formula Presented) G3 with r=4, 6, 7 and 10, whereas the classes of metrics of type D admit Gr (Formula Presented) G3 with r=3, 4, 5 and 6 as the maximal isometry groups. Type O metrics with a perfect fluid source are then found explicitly and are shown to admit a maximal Gr with r=4, 7 and 10. Type D perfect fluid metrics are found explicitly which admit either a maximal G3 or G4. This classification also proves that the only non-null Einstein-Maxwell field admitting a maximal G4 (Formula Presented) G3 is the type D metric (6.7) which is of Segre type [(1, 1)(11)] and is isometric to the McVittie solution.
AB - Metrics admitting a minimal three dimensional Abelian isometry group, G3 are classified according to their Petrov types and metrics, giving all type O and D metrics explicitly, without imposing a source condition. The corresponding maximal Lie algebras for these metrics are obtained and identified as well. The type O metrics admit a maximal Gr (Formula Presented) G3 with r=4, 6, 7 and 10, whereas the classes of metrics of type D admit Gr (Formula Presented) G3 with r=3, 4, 5 and 6 as the maximal isometry groups. Type O metrics with a perfect fluid source are then found explicitly and are shown to admit a maximal Gr with r=4, 7 and 10. Type D perfect fluid metrics are found explicitly which admit either a maximal G3 or G4. This classification also proves that the only non-null Einstein-Maxwell field admitting a maximal G4 (Formula Presented) G3 is the type D metric (6.7) which is of Segre type [(1, 1)(11)] and is isometric to the McVittie solution.
KW - Einstein-Maxwell fields
KW - Lie groups of dimension 3 or more
KW - Metrics
KW - Perfect fluids
KW - Petrov types
UR - http://www.scopus.com/inward/record.url?scp=85079661746&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85079661746&partnerID=8YFLogxK
U2 - 10.1088/2399-6528/aaecb2
DO - 10.1088/2399-6528/aaecb2
M3 - Article
AN - SCOPUS:85079661746
SN - 2399-6528
VL - 2
JO - Journal of Physics Communications
JF - Journal of Physics Communications
IS - 11
M1 - 115011
ER -