= Four-acceleration
{title2=$A^\mu=DU^\mu/d\tau$}
{wiki}
The <four-acceleration> is the <covariant derivative> of <four-velocity> along a massive observer's <worldline>: $A^\mu=dU^\mu/d\tau+\Gamma^\mu_{\nu\rho}U^\nu U^\rho$. In Cartesian <Minkowski spacetime> coordinates the <Christoffel symbols> vanish, leaving the ordinary <proper time> derivative. Differentiating the constant velocity norm gives $U\cdot A=0$; in the instantaneous <rest frame>, $A=(0,\mathbf a)$, so $A\cdot A=-a^2$ with $+---$ <metric signature>. The magnitude $a$ is the <proper acceleration>.
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