  We study extremal non-BPS black holes and strings arising in M-theory
compactifications on Calabi-Yau threefolds, obtained by wrapping M2 branes on
non-holomorphic 2-cycles and M5 branes on non-holomorphic 4-cycles. Using the
attractor mechanism we compute the black hole mass and black string tension,
leading to a conjectural formula for the asymptotic volumes of connected,
locally volume-minimizing representatives of non-holomorphic, even-dimensional
homology classes in the threefold, without knowledge of an explicit metric. In
the case of divisors we find examples where the volume of the representative
corresponding to the black string is less than the volume of the minimal
piecewise-holomorphic representative, predicting recombination for those
homology classes and leading to stable, non-BPS strings. We also compute the
central charges of non-BPS strings in F-theory via a near-horizon $AdS_3$ limit
in 6d which, upon compactification on a circle, account for the asymptotic
entropy of extremal non-supersymmetric 5d black holes (i.e., the asymptotic
count of non-holomorphic minimal 2-cycles).
