  We present a new technique for identifying stellar mass black holes in low
mass X-ray binaries (LMXBs), and apply it to XMM-Newton observations of M31. We
examine X-ray time series variability seeking power density spectra (PDS)
typical of LMXBs accreting at a low accretion rate (which we refer to as Type A
PDS); these are very similar for black hole and neutron star LMXBs. Galactic
neutron star LMXBs exhibit Type A PDS at low luminosities (~10^36--10^37 erg/s)
while black hole LMXBs can exhibit them at luminosities >10^38 erg/s. We
propose that Type A PDS are confined to luminosities below a critical fraction
of the Eddington limit, $l_c$ that is constant for all LMXBs; we have examined
asample of black hole and neutron star LMXBs and find they are all consistent
with $l_c$ = 0.10+/-0.04 in the 0.3--10 keV band. We present luminosity and PDS
data from 167 observations of X-ray binaries in M31 that provide strong support
for our hypothesis. Since the theoretical maximum mass for a neutron star is
\~3.1 M_Sun, we therefore assert that any LMXB that exhibits a Type A PDS at a
0.3--10 keV luminosity greater than 4 x 10^37 erg/s is likely to contain a
black hole primary. We have found eleven new black hole candidates in M31 using
this method. We focus on XMM-Newton observations of RX J0042.4+4112, an X-ray
source in M31 and find the mass of the primary to be 7+/-2 M_Sun, if our
assumptions are correct. Furthermore, RX J0042.4+4112 is consistently bright in
\~40 observations made over 23 years, and is likely to be a persistently bright
LMXB; by contrast all known Galactic black hole LMXBs are transient. Hence our
method may be used to find black holes in known, persistently bright Galactic
LMXBs and also in LMXBs in other galaxies.
