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

Date

2011

Author

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.

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