Chandrasekhar's variational principle

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

References