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 family of tensors and hidden symmetries
Günel, Okan; Sarıoğlu, Bahtiyar Özgür; Department of Physics (2022-8-24)
In this thesis, the symmetries of the spacetimes and symmetry related Killing family of tensors are investigated. The relations between the members of the Killing family of tensors are given. Conserved gravitational charges for the spacetimes are discussed. We calculated conserved charges for Myers-Perry spacetimes using the conserved Kastor-Traschen current obtainable from Killing-Yano tensors in 4, 5, 6, 7, and 8 dimensions. We also studied a Kerr-like metric for rotating spacetimes. We showed that they ...
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.
Nonstandard hulls of ordered vector spaces
Gül, Hasan; Emel'yanov, Eduard; Department of Mathematics (2015)
This thesis undertakes the investigation of ordered vector spaces by applying nonstandard analysis. We introduce and study two types of nonstandard hulls of ordered vector spaces. Norm-nonstandard hulls of ordered Banach spaces are also investigated
Citation Formats
Ç. Menekay, “Killing family of tensors in classical gravitational theories,” M.S. - Master of Science, Middle East Technical University, 2013.