  On the second of November 2019 the black hole X-ray binary MAXI J0637$-$430
went into outburst, at the start of which it was observed in a thermal
``disc-dominated'' state. High photon energy (extending above 10 keV)
observations taken by the NuSTAR telescope reveal that this thermal spectrum
can not be fit by conventional two-component (disc plus corona) approaches
which ignore disc emission sourced from within the plunging region of the black
hole's spacetime. Instead, these models require a third ``additional'' thermal
component to reproduce the data. Using new disc solutions which extend
classical models into the plunging region we show that this ``additional''
thermal emission can be explained self-consistently with photons emitted from
the accretion flow at radii within the innermost stable circular orbit of the
black hole. This represents the second low mass X-ray binary, after MAXI
J1820+070, with a detection of plunging region emission, suggesting that
signatures of this highly relativistic region may well be widespread but not
previously widely appreciated. To allow for a detection of the plunging region,
the black hole in MAXI J0637$-$430 must be at most moderately spinning, and we
constrain the spin to be $a_\bullet < 0.86$ at 99.9$\%$ confidence. We finish
by discussing the observational requirements for the robust detection of this
region.
