Thin shell model revisited

Sijie Gao; Xiaobao Wang

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arXiv · 1412.7899

Thin shell model revisited

Sijie Gao·Xiaobao Wang

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Abstract

We reconsider some fundamental problems of the thin shell model. First, we point out that the "cut and paste" construction does not guarantee a well-defined manifold because there is no overlap of coordinates across the shell. When one requires that the spacetime metric across the thin shell is continuous, it also provides a way to specify the tangent space and the manifold. Other authors have shown that this specification leads to the conservation laws when shells collide. On the other hand, the well-known areal radius $r$ seems to be a perfect coordinate covering all regions of a spherically symmetric spacetime. However, we show by simple but rigorous arguments that $r$ fails to be a coordinate covering a neighborhood of the thin shell if the metric across the shell is continuous. When two spherical shells collide and merge into one, we show that it is possible that $r$ remains to be a good coordinate and the conservation laws hold. To make this happen, different spacetime regions divided by the shells must be glued in a specific way such that some constraints are satisfied. We compare our new construction with the old one by solving constraints numerically.

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Sijie Gao, Xiaobao Wang. 2014-12-26. Thin shell model revisited. https://arxiv.org/abs/1412.7899

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