Eur. Phys. J. C (2013) 73: 2394
https://doi.org/10.1140/epjc/s10052-013-2394-x

Regular Article - Theoretical Physics

Local Lorentz transformation and exact spherically symmetric vacuum solutions in f(T) gravity theories

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

^* e-mail: nashed@bue.edu.eg

Received: 18 December 2012
Revised: 21 March 2013
Published online: 12 April 2013

Abstract

In this paper a non-diagonal, spherically symmetric, tetrad field that contains an arbitrary function, S(r), which corresponds to a local Lorentz transformation, is applied to the field equations of f(T) gravity theories. Analytic vacuum solutions with integration constants are derived. These constants are studied by calculating the total conserved charge associated with each solution. The study shows that the obtained solutions represent the Schwarzschild–Ads spacetime.