3+1 orthogonal and conformal decomposition of the einstein equation and the adm formalism for general relativity

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2011

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Dengiz, Suat

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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.

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Physics.

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http://etd.lib.metu.edu.tr/upload/12612949/index.pdf
https://hdl.handle.net/11511/20446

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Graduate School of Natural and Applied Sciences, Thesis

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Citation Formats

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.