On 5D Black Brane Stabilities from M-theory on Three Parameter Calabi-Yau Threefolds

In this work, we reconsider the study of 5D black branes in M-theory compactifications by means of $\mathcal{N}=2$ supergravity formalism. Precisely, we provide a model relaying on a three parameter Calabi-Yau manifold in the $\mathbb{P}^{1}\times\mathbb{P}^{1}\times\mathbb{P}^{2}$ projective space factorization, referred to as economical model. First, we investigate the stability of 5D BPS and non-BPS black holes obtained from wrapped M2-branes on non-holomorphic two-cycles in such a Calabi-Yau manifold. Then, we approach the stability of 5D black strings derived from wrapped M5-branes on non-holomorphic four-cycles. Among others, we find various stable and unstable black brane solutions depending on the charge regions of the involved moduli space.