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 [Formula: see text] supergravity formalism. Precisely, we provide a model relaying on a three-parameter Calabi–Yau (CY) manifold in the [Formula: see text] 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 nonholomorphic two-cycles in such a CY manifold. Then, we approach the stability of 5D black strings derived from wrapped M5-branes on nonholomorphic four-cycles. Among others, we find various stable and unstable black brane solutions depending on the charge regions of the involved moduli space.