Chandrasekhar potential energy tensor

In astrophysics, Chandrasekhar potential energy tensor provides the gravitational potential of a body due to its own gravity created by the distribution of matter across the body, named after the Indian American astrophysicist Subrahmanyan Chandrasekhar. The Chandrasekhar tensor is a generalization of potential energy in other words, the trace of the Chandrasekhar tensor provides the potential energy of the body.

Definition

The Chandrasekhar potential energy tensor is defined as

where

where

• is the Gravitational constant
• is the self-gravitating potential from Newton's law of gravity
• is the generalized version of
• is the matter density distribution
• is the volume of the body

It is evident that is a symmetric tensor from its definition. The trace of the Chandrasekhar tensor is nothing but the potential energy .

Hence Chandrasekhar tensor can be viewed as the generalization of potential energy.

Chandrasekhar's Proof

Consider a matter of volume with density . Thus

Chandrasekhar tensor in terms of scalar potential

The scalar potential is defined as

then Chandrasekhar proves that

Setting we get , taking Laplacian again, we get .

See also

• Virial theorem
• Chandrasekhar virial equations

References