Table of Contents
Journal of Gravity
Volume 2016 (2016), Article ID 7636493, 8 pages
http://dx.doi.org/10.1155/2016/7636493
Research Article

Transformation Groups for a Schwarzschild-Type Geometry in Gravity

1Department of Physics, Sinop University, 57000 Sinop, Turkey
2Department of Physics, Sakarya University, 54187 Sakarya, Turkey

Received 28 June 2016; Revised 17 October 2016; Accepted 23 October 2016

Academic Editor: Sergei D. Odintsov

Copyright © 2016 Emre Dil and Talha Zafer. 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.

Abstract

We know that the Lorentz transformations are special relativistic coordinate transformations between inertial frames. What happens if we would like to find the coordinate transformations between noninertial reference frames? Noninertial frames are known to be accelerated frames with respect to an inertial frame. Therefore these should be considered in the framework of general relativity or its modified versions. We assume that the inertial frames are flat space-times and noninertial frames are curved space-times; then we investigate the deformation and coordinate transformation groups between a flat space-time and a curved space-time which is curved by a Schwarzschild-type black hole, in the framework of gravity. We firstly study the deformation transformation groups by relating the metrics of the flat and curved space-times in spherical coordinates; after the deformation transformations we concentrate on the coordinate transformations. Later on, we investigate the same deformation and coordinate transformations in Cartesian coordinates. Finally we obtain two different sets of transformation groups for the spherical and Cartesian coordinates.