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- W4300996879 abstract "Any symmetry reduces a second-order differential equation to a first integral: variational symmetries of the action (exemplified by central field dynamics) lead to conservation laws, but symmetries of only the equations of motion (exemplified by scale-invariant hydrostatics) yield first-order {em non-conservation laws} between invariants. We obtain these non-conservation laws by extending Noether's Theorem to non-variational symmetries and present an innovative variational formulation of spherical adiabatic hydrostatics. For the scale-invariant case, this novel synthesis of group theory, hydrostatics, and astrophysics allows us to recover all the known properties of polytropes and define a {em core radius}, inside which polytropes of index $n$ share a common core mass density structure, and outside of which their envelopes differ. The Emden solutions (regular solutions of the Lane-Emden equation) are obtained, along with useful approximations. An appendix discusses the $n=3$ polytrope in order to emphasize how the same mechanical structure allows different thermal structures in relativistic degenerate white dwarfs and zero age main sequence stars." @default.
- W4300996879 created "2022-10-04" @default.
- W4300996879 creator A5011101971 @default.
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- W4300996879 date "2011-12-18" @default.
- W4300996879 modified "2023-09-25" @default.
- W4300996879 title "Scaling Symmetry and Integrable Spherical Hydrostatics" @default.
- W4300996879 doi "https://doi.org/10.48550/arxiv.1112.4223" @default.
- W4300996879 hasPublicationYear "2011" @default.
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