Four-force

F = {dp \over d	au}

.

Since

p = mU \,

where ''m'' is the Invariant Mass and ''

U \,

'' is the Four-velocity , we can relate the four-force with the Four-acceleration as like Newton's Second Law :

:

F = mA = \left(\gamma \dot \gamma mc,\gamma\mathbf f
ight)

.

Here, m is the Invariant Mass and

\mathbf f=m\left(\dot\gamma\mathbf u+\gamma\mathbf{\dot u}
ight)

.

In General Relativity the relation between four-force, and Four-acceleration remains the same, but the elements of the four-force are related to the elements of the Four-momentum through a Covariant Derivative with respect to proper time.

:

F^\lambda := rac{Dp^\lambda }{d	au} = rac{dp^\lambda }{d	au } + \Gamma^\lambda {}_{\mu 
u}U^\mu p^
u

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