Variations of Gauss-Codazzi-Ricci Equations in Kaluza-Klein Reduction (String Theory) and Cauchy Problem (General Relativity)
نویسنده
چکیده
We find a kind of variations of Gauss-Codazzi-Ricci equations suitable for Kaluza-Klein reduction and Cauchy problem. Especially the counterpart of extrinsic curvature tensor has antisymmetric part as well as symmetric one. If the dependence of metric tensor on reduced dimensions is negligible it becomes a pure antisymmetric tensor. PACS:03.70;11.15
منابع مشابه
Kaluza-Klein dimensional reduction and Gauss-Codazzi-Ricci equations
In this paper we imitate the traditional method which is used customarily in the General Relativity and some mathematical literatures to derive the Gauss-Codazzi-Ricci equations for dimensional reduction. It would be more distinct concerning geometric meaning than the vielbein method. Especially, if the lower dimensional metric is independent of reduced dimensions the counterpart of the symmetr...
متن کاملUniversal Features of Dimensional Reduction Schemes from General Covariance Breaking
Many features of dimensional reduction schemes are determined by the breaking of higher dimensional general covariance associated with the selection of a particular subset of coordinates. By investigating residual covariance we introduce lower dimensional tensors, that successfully generalize to one side Kaluza-Klein gauge fields and to the other side extrinsic curvature and torsion of embedded...
متن کاملSNUTP 96-117 4-Dimensional Kaluza-Klein Approach to General Relativity in the (2,2)-Splitting of Spacetimes
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 4dimensional spacetime, which is viewed as a local product of a (1+1)dimensional base manifold and a 2-dimensional fibre space. In this KaluzaKlein formalism we find that general relativity of 4-dimensional spacetimes can be interpreted in a natural wa...
متن کاملBrane-world Kaluza-Klein Reductions and Branes on the Brane
We present a systematic study of a new type of consistent “Brane-world Kaluza-Klein Reduction,” which describe fully non-linear deformations of co-dimension one objects that arise as solutions of a large class of gauged supergravity theories in diverse dimensions, and whose world-volume theories are described by ungauged supergravities with one half of the original supersymmetry. In addition, w...
متن کاملThe Cosmological Constant Problem and Kaluza-Klein Theory
We present technical results which extend previous work and show that the cosmological constant of general relativity is an artefact of the reduction to 4D of 5D Kaluza-Klein theory (or 10D superstrings and 11D supergravity). We argue that the distinction between matter and vacuum is artificial in the context of ND field theory. The concept of a cosmological “constant” (which measures the energ...
متن کامل