Non-Supersymmetric Attractors
Kevin Goldstein, Norihiro Iizuka, Rudra P. Jena, Sandip P. Trivedi
TL;DR
The paper demonstrates that the attractor mechanism extends beyond supersymmetric (BPS) black holes to non-supersymmetric extremal black holes in four-dimensional gravity with gauge fields and moduli, provided two conditions on an effective potential V_eff are satisfied. By formulating V_eff from the gauge couplings and charges, the authors derive that horizon values φ0 are fixed by ∂_i V_eff(φ0)=0 and require a positive definite Hessian, ensuring the scalars are drawn to φ0 regardless of asymptotic values. They support these claims with a perturbative analysis around extremal RN, exact mappings in special cases, and numerical results, showing the entropy S_BH = π b_H^2 depends only on charges. The results generalize to AdS and higher dimensions and offer a framework for understanding non-supersymmetric attractors, with potential implications for non-SUSY flux vacua and entropy counting in string theory contexts.
Abstract
We consider theories with gravity, gauge fields and scalars in four-dimensional asymptotically flat space-time. By studying the equations of motion directly we show that the attractor mechanism can work for non-supersymmetric extremal black holes. Two conditions are sufficient for this, they are conveniently stated in terms of an effective potential involving the scalars and the charges carried by the black hole. Our analysis applies to black holes in theories with ${\cal N} \le 1$ supersymmetry, as well as non-supersymmetric black holes in theories with ${\cal N} = 2$ supersymmetry. Similar results are also obtained for extremal black holes in asymptotically Anti-de Sitter space and in higher dimensions.