= Horizon flux inequality for causal matter
{title2=$E-\Omega_HL\ge0$}
For a future-directed causal four-momentum $p$ crossing a future <Killing horizon> with generator $\xi=t+\Omega_H\varphi$, the Lorentzian inner product obeys $p\cdot\xi\le0$. With $E=-p\cdot t$ and $L=p\cdot\varphi$, this is $E\ge\Omega_HL$. A massive particle has strict inequality. The same bound follows in the nonextremal quasistationary regime from the <Physical-process first law for a rotating black hole> and the <second law of black-hole mechanics>. Negative Killing energy in a <Penrose process> is allowed, but its angular momentum must satisfy this bound.
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