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Approximate solution of a Thomas-Fermi model equation for bulk self-gravitating stellar objects in two dimensions. (English) Zbl 1358.85003

Summary: Direct variational methods are used to find simple approximate solutions of the Thomas-Fermi equations describing the properties of self-gravitating radially symmetric stellar objects both in the non-relativistic and ultra-relativistic cases. The approximate solutions are compared and shown to be in good agreement with exact and numerically obtained solutions.

MSC:

85A15 Galactic and stellar structure
49S05 Variational principles of physics
49K20 Optimality conditions for problems involving partial differential equations
76Y05 Quantum hydrodynamics and relativistic hydrodynamics
85-08 Computational methods for problems pertaining to astronomy and astrophysics
83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)
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References:

[1] De S and Chakrabarty S 2015 Thomas–Fermi model for a bulk self-gravitating stellar object in two dimensions Eur. J. Phys.36 055006 · Zbl 1332.85004
[2] Parwani R R 2004 An approximate expression for the large angle period of a simple pendulum Eur. J. Phys.25 37–9 · Zbl 1162.70300
[3] Wan F Y M 1995 Introduction to the Calculus of Variations and its Applications (New York: Chapman and Hall) · Zbl 0843.49001
[4] Komzsik L 2009 Applied Calculus of Variations for Engineers (Boca Raton, FL: CRC Press/Taylor and Francis Group) · Zbl 1197.49001
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