TY - JOUR

T1 - Classification of plane-symmetric Lorentzian manifolds according to their homotheties and metrics

AU - Bashir, M Ziad

AU - Ehsan, Sadia

PY - 2008

Y1 - 2008

N2 - Plane-symmetric Lorentzian manifolds are classified according to their homothetic vector fields and metrics or classes of metrics. It is found that these manifolds can admit 4, 5, 7 and 11 dimensional homothetic Lie algebras. Explicit self-similar metrics are obtained corresponding to the homothetic Lie algebras of dimensions greater than or equal to five. For four-dimensional homothetic Lie algebras, there appear classes of self-similar metrics, with metric coefficients related by non-linear differential constraints. Explicit examples are provided to ensure the existence of proper homothetic vector fields in the cases where the metrics are given implicitly. Later, using this classification, self-similar metrics are found which represent perfect-fluid solutions of the Einstein field equations.

AB - Plane-symmetric Lorentzian manifolds are classified according to their homothetic vector fields and metrics or classes of metrics. It is found that these manifolds can admit 4, 5, 7 and 11 dimensional homothetic Lie algebras. Explicit self-similar metrics are obtained corresponding to the homothetic Lie algebras of dimensions greater than or equal to five. For four-dimensional homothetic Lie algebras, there appear classes of self-similar metrics, with metric coefficients related by non-linear differential constraints. Explicit examples are provided to ensure the existence of proper homothetic vector fields in the cases where the metrics are given implicitly. Later, using this classification, self-similar metrics are found which represent perfect-fluid solutions of the Einstein field equations.

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U2 - 10.1393/ncb/i2008-10518-6

DO - 10.1393/ncb/i2008-10518-6

M3 - Article

VL - 123

SP - 71

EP - 83

JO - Nuovo Cimento della Societa Italiana di Fisica. B, General Physics, Relativity, Astronomy and Mathematical Physics and Methods

JF - Nuovo Cimento della Societa Italiana di Fisica. B, General Physics, Relativity, Astronomy and Mathematical Physics and Methods

IS - 1

ER -