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Chandrasekhar's variational principle

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In astrophysics, Chandrasekhar's variational principle provides the stability criterion for a static barotropic star, subjected to radial perturbation, named after the Indian American astrophysicist Subrahmanyan Chandrasekhar.

Statement

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A baratropic star with and is stable if the quantity

is non-negative for all real functions that conserve the total mass of the star .

where

  • is the coordinate system fixed to the center of the star
  • is the radius of the star
  • is the volume of the star
  • is the unperturbed density
  • is the small perturbed density such that in the perturbed state, the total density is
  • is the self-gravitating potential from Newton's law of gravity
  • is the Gravitational constant

[1][2][3]

References

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  1. ^ Chandrasekhar, S. "A general variational principle governing the radial and the non-radial oscillations of gaseous masses." VI. Ellipsoidal Figures of Equilibrium 1.2 (1960).
  2. ^ Chandrasekhar, Subrahmanyan. Hydrodynamic and hydromagnetic stability. Courier Corporation, 2013.
  3. ^ Binney, James, and Scott Tremaine. Galactic dynamics. Princeton university press, 2011.