  In numerical relativity, spacetimes involving compact strongly gravitating
objects are constructed as numerical solutions of Einstein's equations. Success
of such a process strongly depends on the availability of appropriate
coordinates, which are typically constructed dynamically. A very robust
coordinate choice is a so-called moving puncture gauge, commonly used for
numerical simulations of black hole spacetimes. Nevertheless it is known to
fail for evolving near-critical Brill wave data. We construct a new
`quasi-maximal' slicing condition and demonstrate that it exhibits better
behavior for such data. This condition is based on the 1+log slicing with an
additional source term derived from maximal slicing. It is relatively simple to
implement in existing moving puncture codes and computationally inexpensive. We
also illustrate the properties of constructed spacetimes based on
gauge-independent quantities in compactified spacetime diagrams. These
invariants are also used to show how created black holes settle down to a
Schwarzschild black hole.

General Relativity and Quantum Cosmology