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
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 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).Chandrasekhar, Subrahmanyan. Hydrodynamic and hydromagnetic stability. Courier Corporation, 2013.Binney, James, and Scott Tremaine. Galactic dynamics. Princeton university press, 2011.
References