1996/11/21 by J. H. Yoon, Yoon, J. H. · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Noncommutative and Quantum Gravity Theories #gr-qc #hep-th
paper · pdf · doi:10.48550/arxiv.gr-qc/9611050
37 pages, RevTex, contains 1 ps file for one figure. Downloading the PostScript file is recommended for Web users. No change was made except this comment
arxiv created 1996/12/03 · arxiv updated 2009/11/30
We propose a Kaluza-Klein approach to general relativity of 4-dimensional spacetimes. This approach is based on the (2,2)-splitting of a generic 4-dimensional spacetime, which is viewed as a local product of a (1+1)-dimensional base manifold and a 2-dimensional fibre space. In this Kaluza-Klein formalism we find that general relativity of 4-dimensional spacetimes can be interpreted in a natural way as a (1+1)-dimensional gauge theory. In a gauge where the (1+1)-dimensional metric can be written as the Polyakov metric, the action is describable as a (1+1)-dimensional Yang-Mills type gauge theory action coupled to a (1+1)-dimensional non-linear sigma field and a scalar field, subject to the constraint equations associated with the diffeomorphism invariance of the (1+1)-dimensional base manifold. Diffeomorphisms along the fibre directions show up as the Yang-Mills type gauge symmetries, giving rise to the Gauss-law constraints. We also present the Einstein's equations in the Polyakov gauge and discuss them from the (1+1)-dimensional gauge theory point of view. Finally we show that this Kaluza-Klein formalism is closely related to the null hypersurface formalism of general relativity.