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Advances in High Energy Physics
Volume 2014, Article ID 857936, 9 pages
Research Article

Exact Axially Symmetric Solution in Gravity Theory

1Centre for Theoretical Physics, The British University in Egypt, Sherouk City 11837, P.O. Box 43, Cairo, Egypt
2Mathematics Department, Faculty of Science, Ain Shams University, Cairo 11566, Egypt

Received 22 August 2013; Revised 29 January 2014; Accepted 12 February 2014; Published 16 March 2014

Academic Editor: George Siopsis

Copyright © 2014 Gamal G. L. Nashed. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.


A general tetrad field with sixteen unknown functions is applied to the field equations of gravity theory. An analytic vacuum solution is derived with two constants of integration and an angle that depends on the angle coordinate and radial coordinate . The tetrad field of this solution is axially symmetric and the scalar torsion vanishes. We calculate the associated metric of the derived solution and show that it represents Kerr spacetime. Finally, we show that the derived solution can be described by two local Lorentz transformations in addition to a tetrad field that is the square root of the Kerr metric. One of these local Lorentz transformations is a special case of Euler’s angles and the other represents a boost when the rotation parameter vanishes.