TL;DR
This paper analyzes the geometry of spherical shells in spacetime using two coordinate systems, calculating extrinsic curvatures and discussing applications to Israel junction conditions.
Contribution
It provides a detailed comparison of coordinate systems and computes extrinsic curvatures for spherical shells, enhancing understanding of junction conditions in general relativity.
Findings
Extrinsic curvatures are explicitly calculated in both coordinate systems.
Transformations between coordinate systems are characterized.
Applications to Israel junction conditions are discussed.
Abstract
Geometry of the spacetime with a spherical shell embedded in it is studied in two coordinate systems - in Kodama-Schwarzschild coordinates and in Gaussian normal coordinates. We consider transformations between the coordinate systems as in the 4D spacetime so as at the surface swept in the spacetime by the spherical shell. Extrinsic curvatures of the surface swept by the shell are calculated in both coordinate systems. Applications to the Israel junction conditions are discussed.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Relativity and Gravitational Theory · Cosmology and Gravitation Theories