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4-acceleration (four-acceleration) is a four-vector which in special relativity is the proper time derivative of 4-velocity.

When curvalinear coordinates are used such as in general relativity, the acceleration 4-vector is the covariant derivative of 4-velocity with respect to proper time (see operator of proper-time-derivative)

It relates to the force Four-force by Newton's second law

where the mass is an invariant.

And in the Absence of a 4-force this

gives the geodesic equation