This paper argues that coupling the Abelian Higgs model to gravity with a negative cosmological constant leads to black holes that spontaneously break gauge symmetry via a charged scalar condensate near their horizon. This suggests that black holes can superconduct. The Abelian Higgs model is described by the Lagrangian: $$ 16\pi G_{N}\mathcal{L}=R-\frac{6}{L^{2}}-\frac{1}{4}F_{\mu\nu}^{2}-|\partial_{\mu}\psi-i q A_{\mu}\psi|^{2}-m^{2}|\psi|^{2}, $$ where $ G_N $ is Newton's constant, $ L $ is the AdS radius, $ q $ is the charge of the scalar field, and $ m $ is its mass. The effective mass of the scalar field is $ m_{\mathrm{eff}}^{2} = m^{2} + g^{tt} q^{2} \Phi^{2} $, which becomes negative near the horizon if $ \Phi $ is non-zero, leading to spontaneous symmetry breaking. The analysis focuses on Reissner-Nordstrom black holes in AdS space, where the scalar field $ \psi $ can develop a non-zero value slightly outside the horizon. The paper discusses the conditions under which this symmetry breaking occurs, including the role of the black hole's charge, temperature, and the scalar field's mass. It also explores the implications for superconductivity, noting that the mechanism described here uses only renormalizable interactions, unlike the non-renormalizable coupling in the earlier proposal. The paper concludes that the Abelian Higgs model can exhibit spontaneous symmetry breaking near black hole horizons, suggesting that black holes can superconduct when sufficiently cold. The results are discussed in the context of holography and the AdS/CFT correspondence, with implications for understanding superconductivity in strongly correlated systems.This paper argues that coupling the Abelian Higgs model to gravity with a negative cosmological constant leads to black holes that spontaneously break gauge symmetry via a charged scalar condensate near their horizon. This suggests that black holes can superconduct. The Abelian Higgs model is described by the Lagrangian: $$ 16\pi G_{N}\mathcal{L}=R-\frac{6}{L^{2}}-\frac{1}{4}F_{\mu\nu}^{2}-|\partial_{\mu}\psi-i q A_{\mu}\psi|^{2}-m^{2}|\psi|^{2}, $$ where $ G_N $ is Newton's constant, $ L $ is the AdS radius, $ q $ is the charge of the scalar field, and $ m $ is its mass. The effective mass of the scalar field is $ m_{\mathrm{eff}}^{2} = m^{2} + g^{tt} q^{2} \Phi^{2} $, which becomes negative near the horizon if $ \Phi $ is non-zero, leading to spontaneous symmetry breaking. The analysis focuses on Reissner-Nordstrom black holes in AdS space, where the scalar field $ \psi $ can develop a non-zero value slightly outside the horizon. The paper discusses the conditions under which this symmetry breaking occurs, including the role of the black hole's charge, temperature, and the scalar field's mass. It also explores the implications for superconductivity, noting that the mechanism described here uses only renormalizable interactions, unlike the non-renormalizable coupling in the earlier proposal. The paper concludes that the Abelian Higgs model can exhibit spontaneous symmetry breaking near black hole horizons, suggesting that black holes can superconduct when sufficiently cold. The results are discussed in the context of holography and the AdS/CFT correspondence, with implications for understanding superconductivity in strongly correlated systems.