  Relativistic strong-field ionization of hydrogen-like atoms or ions in a
constant crossed electromagnetic field is studied. The transition amplitude is
formulated within the strong-field approximation in G\"oppert-Mayer gauge, with
initial and final electron states being described by the corresponding
Dirac-Coulomb and Dirac-Volkov wave functions, respectively. Coulomb
corrections to the electron motion during tunneling are taken into account by
adjusting an established method to the present situation. Total and
energy-differential ionization rates are calculated and compared with
predictions from other theories in a wide range of atomic numbers and applied
field strengths.
