Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
3+1 orthogonal and conformal decomposition of the einstein equation and the adm formalism for general relativity
Download
index.pdf
Date
2011
Author
Dengiz, Suat
Metadata
Show full item record
Item Usage Stats
58
views
35
downloads
Cite This
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 reconstructed. All the calculations up to chapter 7 are just a review. We propose a method in chapter 7 which gives an interesting relation between the Cotton (Conformal) soliton and the static vacuum solutions. The formulation that we introduce can be extended to find the gradient Cotton soliton and the solutions of Topologically Massive Gravity (TMG) as well as the gradient Ricci soliton.
Subject Keywords
Physics.
URI
http://etd.lib.metu.edu.tr/upload/12612949/index.pdf
https://hdl.handle.net/11511/20446
Collections
Graduate School of Natural and Applied Sciences, Thesis
Suggestions
OpenMETU
Core
İnvestigating the semileptonic B to K1(1270,1400) decays in QCD sum rules
Dağ, Hüseyin; Zeyrek, Mehmet Tevfik; Department of Physics (2010)
Quantum Chromodynamics(QCD) is part of the Standard Model(SM) that describes the interaction of fundamental particles. In QCD, due to the fact that strong coupling constant is large at low energies, perturbative approaches do not work. For this reason, non-perturbative approaches have to be used for studying the properties of hadrons. Among several non-perturbative approaches, QCD sum rules is one of the reliable methods which is applied to understand the properties of hadrons and their interactions.\ In th...
A physical model for dimensional reduction and its effects on the observable parameters of the universe
Karaca, Koray; Bayın, Selçuk; Department of Physics (2005)
In this thesis, assuming that higher spatial dimensions existed only during the inflationary prematter phases of the universe, we construct a (1+D)-dimensional (D>3), nonsingular, homogeneous and isotropic Friedmann model for dimensional reduction. In this model, dimensional reduction occurs in the form of a phase transition that follows from a purely thermodynamical consideration that the universe heats up during the inflationary prematter phases. When the temperature reaches its Planck value Tpl,D, which ...
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...
Numerical studies of the electronic properties of low dimensional semiconductor heterostructures
Dikmen, Bora; Tomak, Mehmet; Department of Physics (2004)
An efficient numerical method for solving Schrödinger's and Poisson's equations using a basis set of cubic B-splines is investigated. The method is applied to find both the wave functions and the corresponding eigenenergies of low-dimensional semiconductor structures. The computational efficiency of the method is explicitly shown by the multiresolution analysis, non-uniform grid construction and imposed boundary conditions by applying it to well-known single electron potentials. The method compares well wit...
Calculation of the Raman frequencies using volume data in various phases of solid nitrogen and benzene
Çetinbaş İşeri, Esin; Yurtseven, Hasan Hamit; 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...
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
S. Dengiz, “3+1 orthogonal and conformal decomposition of the einstein equation and the adm formalism for general relativity,” M.S. - Master of Science, Middle East Technical University, 2011.