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 ${𝕎\mathbb{P}}^4(\omega ,1,1,1,1)\times {\mathbb{P}}^1$. Using the $N=2$ supergravity formalism in five dimensions, we examine the BPS and non-BPS solutions 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${\mathbb{P}}^4$with$\omega =1$. Using extended black hole entropies, we evaluate the temperature involving a minimal value for${\mathbb{P}}^4$. 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 ${\mathbb{P}}^4$. 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.

在这项工作中，我们重新考虑卡拉比-丘三重 M 理论压缩中黑洞和黑弦的研究，被认为是加权射影空间乘积中超曲面的完全交集，由下式给出${𝕎\mathbb{P}}^4（\omega ,1,1,1,1）\times {\mathbb{P}}^1$。使用$氮=2$在五个维度的超重力形式主义中，我们通过在卡拉比-丘几何中将 M 膜包裹在适当的循环上来检查 BPS 和非 BPS 解决方案。对于黑洞情况，我们计算某些热力学量。特别地，我们计算熵取对应于普通射影空间的最大值${\mathbb{P}}^4$和$\omega =1$。使用扩展黑洞熵，我们评估涉及最小值的温度${\mathbb{P}}^4$。然后，我们通过复合因子来逼近非 BPS 黑洞的稳定性。在允许的电荷区域中，我们表明这种状态是不稳定的。对于黑弦解，我们计算张力取对应于的最小值${\mathbb{P}}^4$。计算复合因子，我们表明相关的非 BPS 黑弦态在模空间允许的磁荷区域中是稳定的。