TY - JOUR
T1 - Classification of Cylindrically Symmetric Static Spacetimes according to Their Ricci Collineations
AU - Qadir, Asghar
AU - Saifullah, K.
AU - Ziad, M.
N1 - Funding Information:
This work was supported in part by Pakistan Science Foundation under Project No. C-QU/MATHS (21) and by the Quaid-i-Azam University Research Fund. One of the authors (KS) gratefully acknowledges the excellent research facilities at the Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, where a part of this work was done during two short term visits.
PY - 2003/11
Y1 - 2003/11
N2 - A complete classification of cylindrically symmetric static Lorentzian manifolds according to their Ricci collineations (RCs) is provided. The Lie algebras of RCs for the non-degenerate Ricci tensor have dimensions 3 to 10, excluding 8 and 9. For the degenerate tensor the algebra is mostly but not always infinite dimensional; there are cases of 10-, 5-, 4- and 3-dimensional algebras. The RCs are compared with the Killing vectors (KVs) and homothetic motions (HMs). The (non-linear) constraints corresponding to the Lie algebras are solved to construct examples which include some exact solutions admitting proper RCs. Their physical interpretation is given. The classification of plane symmetric static spacetimes emerges as a special case of this classification when the cylinder is unfolded.
AB - A complete classification of cylindrically symmetric static Lorentzian manifolds according to their Ricci collineations (RCs) is provided. The Lie algebras of RCs for the non-degenerate Ricci tensor have dimensions 3 to 10, excluding 8 and 9. For the degenerate tensor the algebra is mostly but not always infinite dimensional; there are cases of 10-, 5-, 4- and 3-dimensional algebras. The RCs are compared with the Killing vectors (KVs) and homothetic motions (HMs). The (non-linear) constraints corresponding to the Lie algebras are solved to construct examples which include some exact solutions admitting proper RCs. Their physical interpretation is given. The classification of plane symmetric static spacetimes emerges as a special case of this classification when the cylinder is unfolded.
KW - Cylindrical symmetry
KW - Ricci collineation
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U2 - 10.1023/A:1026238724400
DO - 10.1023/A:1026238724400
M3 - Article
AN - SCOPUS:0347758761
SN - 0001-7701
VL - 35
SP - 1927
EP - 1975
JO - General Relativity and Gravitation
JF - General Relativity and Gravitation
IS - 11
ER -