Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 357 / 2 / e / Solution

Stationarity makes ${\partial }_t\alpha =0$, whileThe left side of the Bona--Masso slicing condition is thereforeIts right side isEquality requiresSince $\alpha =r/(r+M)$, this is the Stationary Schwarzschild Bona--Masso slicing functionConsequently ${\lim }_{\alpha \to 1}f(\alpha )=0$, as expected in the asymptotically flat region $r\to \infty$.