Non-BPS Black Branes in M-theory over Calabi-Yau Threefolds

[abridged version] We study extremal solutions arising in M-theory compactifications on Calabi-Yau threefolds, focussing on non-BPS attractors for their importance in relation to the Weak Gravity Conjecture. In the low-energy/field theory limit one obtains minimal N=2, D=5 supergravity coupled to Abelian vector multiplets. By making use of the effective black hole potential formalism with Lagrange multipliers and of the Attractor Mechanism, and focussing on two-moduli complete intersection (CICY) or toric hypersurface (THCY) Calabi-Yau threefolds, we investigate the possible non-uniqueness of the attractor solutions, as well as the stability of non-BPS black holes and black strings. In all models taken into consideration, we find that both BPS and non-BPS extremal black hole attractors are always unique for a given, supporting electric charge configuration; moreover, non-BPS black holes are always unstable, and thus they decay into constituent BPS/anti-BPS pairs. For what concerns extremal black strings, we confirm uniqueness also for non-BPS strings in two-moduli CICY models. On the other hand, we discover multiple non-BPS extremal black string attractors (with different tensions) in most of the two-moduli THCY models, and we determine the corresponding magnetic configurations supporting them; this indicates the existence of volume-minimizing representatives in the same homology class having different values of their local minimal volume. Moreover, we find that non-BPS black strings, both for single and multiple solutions, are stable and thus enjoy recombination of their constituent BPS/anti-BPS pairs.