= Hydrostatic equilibrium along a Killing vector
{title2=$dp=-(\rho+p)d\log N,\quad N=\sqrt{K^aK_a}$}
For <metric signature> $(+---)$, a stationary <perfect fluid> follows a timelike <Killing vector field> $K$ with <four-velocity> $U=K/N$. Its <Killing-flow four-acceleration> is $U^b\nabla_bU_a=-\nabla_a\log N$. The <relativistic Euler equation> and stationarity of the <pressure> give the displayed <hydrostatic equilibrium> equation. This uses stationarity along $K$ and does not require hypersurface orthogonality.
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