Behaviors of black holes and black strings in M-theory on Calabi–Yau manifolds

In this work, we reconsider the study of black holes and black strings in the compactification of M-theory on a Calabi–Yau three-fold, considered as a complete intersection of hypersurfaces in a product of weighted projective spaces given by [Formula: see text]. Using the [Formula: see text] supergravity formalism in five dimensions, we examine the BPS and non-BPSsolutions by wrapping M-branes on appropriate cycles in such a Calabi–Yau geometry. For the black hole case, we compute certain thermodynamical quantities. In particular, we calculate the entropy taking a maximal value corresponding to the ordinary projective space [Formula: see text] with [Formula: see text]. Using extended black hole entropies, we evaluate the temperature involving a minimal value for [Formula: see text]. Then, we approach the stability of the non-BPS black holes via the recombination factor. In the allowed electric charge regions, we show that such states are unstable. For the black string solutions, we calculate the tension taking a minimal value corresponding to [Formula: see text]. Computing the recombination factor, we show that the associated non-BPS black string states are stable in the allowed magnetic charge regions of the moduli space.