Surface Layers in General Relativity and Their Relation to Surface Tensions

Details Surface Layers in General Relativity and Their Relation to Surface Tensions Surface Layers in General Relativity and Their Relation to Surface Tensions

2001-05-28

arxiv.org/abs/gr-qc/0105106v1

Gen.Rel.Grav.16:1053-1061,1984

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

12 pages, LaTeX, no figure

Scientific paper

10.1007/BF00760644

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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