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Surface Layers in General Relativity and Their Relation to Surface Tensions

H. -J. Schmidt
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Abstract

For a thin shell, the intrinsic 3-pressure will be shown to be analogous to -A, where A is the classical surface tension: First, interior and exterior Schwarzschild solutions will be matched together such that the surface layer generated at the common boundary has no gravitational mass; then its intrinsic 3-pressure represents a surface tension fulfilling Kelvin's relation between mean curvature and pressure difference in the Newtonian limit. Second, after a suitable definition of mean curvature, the general relativistic analogue to Kelvin's relation will be proven to be contained in the equation of motion of the surface layer.

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H. -J. Schmidt. 2001-05-28. Surface Layers in General Relativity and Their Relation to Surface Tensions. https://doi.org/10.1007/bf00760644

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