Required math: algebra
Required physics: special relativity
Reference: Moore, Thomas A., A General Relativity Workbook, University Science Books (2013) – Chapter 4; Problems 4.11.
The four-velocity has the property that, for any object with a non-zero rest mass, (For a photon, four-velocity cannot be defined.). If we define the four-acceleration as
then if we take the derivative of the square of the four-velocity, we get
Thus for any object with a non-zero rest mass, the four-velocity is orthogonal to the four-acceleration.