Hypersurface homogeneous locally rotationally symmetric spacetimes admitting conformal symmetries

Abstract

All hypersurface homogeneous locally rotationally symmetric spacetimes which admit conformal symmetries are determined and the symmetry vectors are given explicitly. It is shown that these spacetimes must be considered in two sets. One set containing Ellis Class II and the other containing Ellis Class I, III LRS spacetimes. The determination of the conformal algebra in the first set is achieved by systematizing and completing results on the determination of CKVs in 2+2 decomposable spacetimes. In the second set new methods are developed. The results are applied to obtain the classification of the conformal algebra of all static LRS spacetimes in terms of geometrical variables. Furthermore all perfect fluid nontilted LRS spacetimes which admit proper conformal symmetries are determined and the physical properties some of them are discussed.

15 pages; to appear in Classical Quantum Gravity; some misprints in Tables 3,5 and in section 4 corrected

References in corpus (5)

• Symmetries of Bianchi I space-times
• Invariant construction of solutions to Einstein's field equations - LRS perfect fluids II
• Computation of the conformal algebra of 1+3 decomposable spacetimes
• Invariant construction of solutions to Einstein`s field equations - LRS perfect fluids I
• Kinematic self-similar locally rotationally symmetric models

Cited by in corpus (9)

• Topologically non-trivial configurations in the 4d Einstein--nonlinear $\sigma$-model system
• Conformally symmetric vacuum solutions of the gravitational field equations in the brane-world models
• Exact solutions of Bianchi I spacetimes which admit Conformal Killing vectors
• Ricci and matter collineations of locally rotationally symmetric space-times
• Perfect Fluid LRS Bianchi I with Time Varying Constants
• Constructing the CKVs of Bianchi III and V spacetimes
• The reduction of Laplace equation in certain Riemannian spaces and the resulting Type II hidden symmetries
• On homothetic Killing vectors in stationary axisymmetric vacuum spacetimes
• Integrability of the Einstein-nonlinear $SU(2)$ $\sigma$-model in a nontrivial topological sector