Quaternionic formalism of curvature space-time and Einstein field equation
Loading...
Date
2019-08
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
G.B. Pant University of Agriculture and Technology, Pantnagar - 263145 (Uttarakhand)
Abstract
In present work, the four-dimensional quaternionic algebra has been used to describing the space-time geometry in curvature form. The properties of pure quaternion are expressed using the transformation of vector basis from one frame to another. Further, we have expressed the transformation of quaternionic variable with the help of basis transformation of quaternion. The transformation of quaternionic scalar and vector derivatives has been shown. We deduced the quaternionic covariant derivative that explains the change in quaternionic components with respect to scalar and vector components. We have also derived covariant derivative for quaternionic tensor of rank-2. An additional term appeared in the transformation known as quaternionic Christoffel symbol which explain the change from one tangent plane to another. The quaternionic metric tensor has been discussed to describing the line element in quaternionic curved space-time. We also expressed the quaternionic geodesic equation for the curved spacetime. We deduced the expression for Christoffel symbol and the Riemannian Christoffel
curvature tensor in terms of quaternionic metric tensor. We have also described the energymomentum tensor in terms of quaternion. Finally, form these expressions we have proposed the quaternionic form of Einstein field equation.
Description
Keywords
null