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