Conserved charges in asymptotically (anti)-de sitter spacetime

Güllü, İbrahim
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 Einstein-Gauss-Bonnet model is studied. The equations of motion are calculated by solving the generic action at quadratic order. Following this, all energy calculations are renewed for this model. Some useful relations and calculations are shown in Appendix (A-B) parts.


Kaluza-klein reduction of higher curvature gravity models
Kuyrukcu, Halil; Başkal, Sibel; Department of Physics (2010)
The standard Kaluza-Klein theory is reviewed and its basic equations are rewritten in an anholonomic basis. A five dimensional Yang-Mills type quadratic and cubic curvature gravity model is introduced. By employing the Palatini variational principle, the field equations and the stress-energy tensors of these models are presented. Unification of gravity with electromagnetism is achieved through the Kaluza-Klein reduction mechanism. Reduced curvature invariants,field equations and stress-energy tensors in fou...
Dynamic ion behavior in plasma source ion implantation
Bozkurt, Bilge; Bilikmen, Kadri Sinan; Department of Physics (2006)
The aim of this work is to analytically treat the dynamic ion behavior during the evolution of the ion matrix sheath, considering the industrial application plasma source ion implantation for both planar and cylindrical targets, and then to de-velop a code that simulates this dynamic ion behavior numerically. If the sepa-ration between the electrodes in a discharge tube is small, upon the application of a large potential between the electrodes, an ion matrix sheath is formed, which fills the whole inter-ele...
3+1 orthogonal and conformal decomposition of the einstein equation and the adm formalism for general relativity
Dengiz, Suat; Tekin, Bayram; Department of Physics (2011)
In this work, two particular orthogonal and conformal decompositions of the 3+1 dimensional Einstein equation and Arnowitt-Deser-Misner (ADM) formalism for general relativity are obtained. In order to do these, the 3+1 foliation of the four-dimensional spacetime, the fundamental conformal transformations and the Hamiltonian form of general relativity that leads to the ADM formalism, defined for the conserved quantities of the hypersurfaces of the globally-hyperbolic asymptotically flat spacetimes, are recons...
Quantum mechanics on curved hypersurfaces
Olpak, Mehmet Ali; Tekin, Bayram; Department of Physics (2010)
In this work, Schrödinger and Dirac equations will be examined in geometries that confine the particles to hypersurfaces. For this purpose, two methods will be considered. The first method is the thin layer method which relies on explicit use of geometrical relations and the squeezing of a certain coordinate of space (or spacetime). The second is Dirac’s quantization procedure involving the modification of canonical quantization making use of the geometrical constraints. For the Dirac equation, only the fir...
Prolongation structures, backlund transformations and painleve analysis of nonlinear evolution equations
Yurduşen, İsmet; Karasu, Emine Ayşe; Department of Physics (2004)
The Wahlquist-Estabrook prolongation technique and the Painleve analysis, used for testing the integrability of nonlinear evolution equations, are considered and applied both to the Drinfel'd-Sokolov system of equations, indeed known to be one of the coupled Korteweg-de Vries (KdV) systems, and Kersten-Krasil'shchik coupled KdV-mKdV equations. Some new Backlund transformations for the Drinfel'd-Sokolov system of equations are also found.
Citation Formats
İ. Güllü, “Conserved charges in asymptotically (anti)-de sitter spacetime,” M.S. - Master of Science, Middle East Technical University, 2005.