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Bona-Masso slicing conditions and the lapse close to black-hole punctures

We consider several families of functions $f(α)$ that appear in the Bona-Masso slicing condition for the lapse function $α$. Focusing on spherically symmetric and time-independent slices we apply these conditions to the Schwarzschild spacetime in order to construct analytical expressions for the lapse $α$ in terms of the areal radius $R$. We then transform to isotropic coordinates and determine the dependence of $α$ on the isotropic radius $r$ in the vicinity of the black-hole puncture. We propose generalizations of previously considered functions $f(α)$ for which, to leading order, the lapse is proportional to $r$ rather than a non-integer power of $r$. We also perform dynamical simulations in spherical symmetry and demonstrate advantages of the above choices in numerical simulations employing spectral methods.