Killing family of tensors in classical gravitational theories

Menekay, Çağatay
In this thesis, the basic properties of the Killing family of tensors (Killing vector, Killing tensors and Killing-Yano tensors) are considered. Their relationship with integrals of motions and conserved gravitational charges are also discussed. The fourth constant of motion of a test particle in Kerr spacetime and its relationship with Killing tensor are reviewed. We have done a similar analysis for the newly discovered solution of Conformal Gravity. Next, the use of Killing-Yano tensors in the procedure for defining conserved gravitational charges is discussed. Finally, a new identity is introduced, and its use in a new approach to overcome a shortcoming of the former construction is given.


Killing-Yano tensors
Nurbaki, Ali Nur; Başkal, Sibel; Department of Physics (2010)
By using the concept of isometry Killing vectors were introduced. Generalizing the Killing vectors Killing tensors of rank two were briefly introduced. Their metrical properties have been dealt.With this path Killing – Yano tensors were introduced as being some hidden space-time symmetries and also square roots of Killing tensors of rank two. Also physical importance of Killing – Yano tensors were briefly introduced. A calculation for 4D pp-wave metric is reviewed. Standart 5-D Kaluza- Klein theory is rewie...
Seven, Ahmet İrfan (2015-02-01)
In the structural theory of cluster algebras, a crucial role is played by a family of integer vectors, called c-vectors, which parametrize the coefficients. It has recently been shown that each c-vector with respect to an acyclic initial seed is a real root of the corresponding root system. In this paper, we obtain an interpretation of this result in terms of symmetric matrices. We show that for skew-symmetric cluster algebras, the c-vectors associated with any seed defines a quasi-Cartan companion for the ...
Conserved charges in asymptotically (anti)-de sitter spacetime
Güllü, İbrahim; Tekin, Bayram; Department of Physics (2005)
In this master̕s thesis, the Killing vectors are introduced and the Killing equation is derived. Also, some information is given about the cosmological constant. Then, the Abbott-Deser (AD) energy is reformulated by linearizing the Einstein equation with cosmological constant. From the linearized Einstein equation, Killing charges are derived by using the properties of Killing vectors. Using this formulation, energy is calculated for some specific cases by using the Schwarzschild-de Sitter metric. Last, the...
BASKAL, S; DERELI, T (IOP Publishing, 1993-04-01)
The variational field equations and the covariantly conserved energy-momentum tensor of a higher-derivative effective Yang-Mills theory are given. A class of static spherically symmetric gauge field configurations that follow from the Wu-Yang ansatz is considered.
All timelike supersymmetric solutions of three-dimensional half-maximal supergravity
DEĞER, NİHAT SADIK; Moutsopoulos, George; Samtleben, Henning; Sarıoğlu, Bahtiyar Özgür (2015-06-22)
We first classify all supersymmetric solutions of the 3-dimensional half-maximal ungauged supergravity that possess a timelike Killing vector by considering their identification under the complexification of the local symmetry of the theory. It is found that only solutions that preserve 16/2(n), 1 <= n <= 3 real supersymmetries are allowed. We then classify supersymmetric solutions under the real local symmetry of the theory and we are able to solve the equations of motion for all of them. It is shown that ...
Citation Formats
Ç. Menekay, “Killing family of tensors in classical gravitational theories,” M.S. - Master of Science, Middle East Technical University, 2013.