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Advances in High Energy Physics
Volume 2016 (2016), Article ID 5632734, 6 pages
http://dx.doi.org/10.1155/2016/5632734
Research Article

Kodama-Schwarzschild versus Gaussian Normal Coordinates Picture of Thin Shells

Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow 119991, Russia

Received 6 September 2016; Accepted 2 November 2016

Academic Editor: S. Habib Mazharimousavi

Copyright © 2016 Mikhail Z. Iofa. 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.

Abstract

Geometry of the spacetime with a spherical shell embedded in it is studied in two coordinate systems: Kodama-Schwarzschild coordinates and Gaussian normal coordinates. We find explicit coordinate transformation between the Kodama-Schwarzschild and Gaussian normal coordinate systems. We show that projections of the metrics on the surface swept by the shell in the 4D spacetime in both cases are identical. In the general case of time-dependent metrics we calculate extrinsic curvatures of the shell in both coordinate systems and show that the results are identical. Applications to the Israel junction conditions are discussed.