Fast orbital decays of black hole X-ray binaries: XTE J1118+480 and
  A0620--00
  We present new 10.4m-GTC/OSIRIS spectroscopic observations of the black hole
X-ray binary \mbox{XTE J1118+480} that confirm the orbital period decay at
$\dot P=-1.90\pm0.57$ ms yr$^{-1}$. This corresponds to a period change of
$-0.88\pm0.27$ $\mu $s per orbital cycle. We have also collected observations
of the black hole X-ray binary A0620--00 to derive an orbital period derivative
of $\dot P=-0.60\pm0.08$ ms yr$^{-1}$ ($-0.53\pm0.07$ $\mu $s/cycle). Angular
momentum losses due to gravitational radiation are unable to explain these
large orbital decays in these two short-period black hole binaries. The orbital
period decay measured in A0620--00 is very marginally consistent with the
predictions of conventional models including magnetic braking, although
significant mass loss ($\dot M_{\rm BH} / \dot M_2 \le 20\%$) from the system
is required. The fast spiral-in of the star in XTE J1118+480, however, does not
fit any standard model and may be driven by magnetic braking under extremely
high magnetic fields and/or may require an unknown process or non-standard
theories of gravity. This result may suggest an evolutionary sequence in which
the orbital period decay begins to speed up as the orbital period decreases.
This scenario may have an impact on the evolution and lifetime of black hole
X-ray binaries.
