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Numerical studies of gravitational collapse to black holes make use ofapparent horizons, which are intrinsically foliation-dependent. We expose theproblem and discuss possible solutions using the Hawking quasilocal mass. Inspherical symmetry, we present a physically sensible approach to the problem byrestricting to spherically symmetric spacetime slicings. In spherical symmetrythe apparent horizons are gauge-independent in any spherically symmetricfoliation but physical quantities associated with them, such as surface gravityand temperature, are not. The widely used comoving and Kodama foliations, whichare of particular interest, are discussed in detail.

Foliation dependence of black hole apparent horizons in spherical symmetry