Talk detail

Participant	Muhammad, Ziad
Institution	Department of Mathematics and Statistics, Sultan Qaboos University - PO Box 36 - Alkhoud - Muscat - Oman

Session	GT1	Accepted		Order	Time
Talk	Oral abstract	Title	Ricci collineations of Plane symmetric Lorentzian manifolds admitting six isometries
Co-authors
Abstract	Use of symmetry methods for the solution of Einstein field equations is reviewed. In particular plane symmetric Loentzian manifolds admitting six isometries are considered and their Ricci collineations are discussed. Later a comparison of the Lie algebras of the Ricci collineations and of the isometries is made. A few metrics are discussed, where the dimension of the Lie algebras of the Ricci collineations and of the isometries are different.

Session	GT1	Accepted		Order	Time
Talk	Oral abstract	Title	Ricci Collineations of Plane Symmetric Lorentzian Manifolds
Co-authors
Abstract	A brief review of symmetry methods for the classification of Lorentzian manifolds is presented. Ricci collineations (RCs) of some plane symmetric Lorentzian manifolds admitting higher symmetries are then discussed. It is noticed that in the case of degenerate Ricci tensors, there appear many cases of infinite RCs. In the case of non degenerate Ricci tensor, there is a common conception that RCs coincide with the isometries. Examples are demonstrated, where there are more RCs than the isometries in the case of a non-degenerate Ricci tensor of a plane symmetric Lorentzian manifold.

Session	GT4	Accepted		Order	Time
Talk	Oral abstract	Title	On some properties of a Plane fronted Gravitational Wave Solution
Co-authors
Abstract	A plane symmetric solution was presented in MG12, which was called a plane wave solution, whereas, it should have been called (as I understand it now)as a plane fronted gravitational wave solution. This solution has a line singularity and admits a null homothetic vector field. Here, a few properties of this solution are discussed, which include: the nature of its stress energy tensor; and the nature of its geodesics in general and in the neighbourhood of the line sigularity.