Article ID Journal Published Year Pages File Type
1894162 Chaos, Solitons & Fractals 2006 11 Pages PDF
Abstract
A geometric formulation of the gravitation theory on a fractal space-time is given. Then, a connection is introduced on a tangent bundle, the connection coefficients, the Riemann curvature tensor and the Einstein field equations are calculated. We can characterize the “relative resolution parameter” as a 'state scale' of the coordinate system, as compared with Einstein's formulation of the relativity principle, in which the relative speed characterize the movement state of the frame. In such a context, it results, by means of a dilation operator, the equivalence of this model with Einstein's quantum gravity. Through the gravitational instantons synchronization, the correspondence with El Naschie's gravity is established.
Related Topics
Physical Sciences and Engineering Physics and Astronomy Statistical and Nonlinear Physics
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