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Abstract 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 (WGC); M2 branes wrapped on two-cycles give rise to black holes, whereas M5 branes wrapped on four-cycles result in black strings. 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, we obtain the explicit expressions of the attractor moduli for BPS and non-BPS solutions, and we compute the Bekenstein-Hawking black hole entropy and the black string tension. Furthermore, by focussing on one modulus 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 (restricting to doubly-extremal solutions, for simplicity’s sake). 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: this confirms the WGC, for which macroscopic non-supersymmetric solutions are bound to decay. For what concerns extremal black strings, it is well known they are unique in the BPS case; we confirm uniqueness also for non-BPS strings in one-modulus CICY models. On the other hand, we discover multiple non-BPS extremal black string attractors (with different tensions) in most of the one-modulus 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 (doubly-) extremal black strings, both for single and multiple solutions, are kinematically stable against decay into their constituent BPS/anti-BPS pairs; in Calabi-Yau geometry, this means that the volume of the representative corresponding to the black string is less than the volume of the minimal piecewise-holomorphic representative, predicting recombination for those homology classes and thus leading to stable, non-BPS string solutions, which for the WGC are microscopic with small charges. |
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