= Covariant equation with a preferred timelike vector
{title2=$(\eta^{\mu\nu}-\alpha n^\mu n^\nu)\partial_\mu\partial_\nu\phi=0$}
In units $c=1$ and <metric signature> $(-,+,+,+)$, take a fixed unit timelike <vector field> $n$ and $\alpha>0$. The displayed equation for a <scalar field> is tensorial; in arbitrary coordinates use the flat <Levi-Civita connection> in place of ordinary second derivatives. In the rest <inertial frame> of $n$ it becomes $-(1+\alpha)\phi_{tt}+\nabla^2\phi=0$, with characteristic <speed> $1/\sqrt{1+\alpha}$. Its fixed $n$ selects a preferred frame. A boost that does not preserve $n$ is not a symmetry with this background held fixed, although transforming the components of every quantity gives an equivalent coordinate description. This separates <general covariance> from a substantive relativity principle.
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