We investigate the neutral AdS black-hole solution in the consistent D → 4 Einstein-Gauss-Bonnet gravity proposed in [K. Aoki, M.A. Gorji, and S. Mukohyama, Phys. Lett. B810 (2020) 135843] and construct the gravity duals of (2 + 1)-dimensional superconductors with Gauss-Bonnet corrections in the probe limit. We find that the curvature correction has a more subtle effect on the scalar condensates in the s-wave superconductor in (2 + 1)-dimensions, which is different from the finding in the higher-dimensional superconductors that the higher curvature correction makes the scalar hair more difficult to be developed in the full parameter space. However, in the p-wave case, we observe that the higher curvature correction always makes it harder for the vector condensates to form in various dimensions. Moreover, we note that the higher curvature correction results in the larger deviation from the expected relation in the gap frequency ωg/Tc ≈ 8 in both (2 + 1)-dimensional s-wave and p-wave models.

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We establish the existence of stationary clouds of massive test scalar fields around Kerr-MOG black holes. By solving the Klein–Gordon equation numerically, we present the existence lines of the clouds in the parameter space of the Kerr-MOG black holes, and investigate the effect of the MOG parameter on the rich structure of scalar clouds. We observe that the MOG parameter leads to the split of the existence lines for the scalar clouds, and the larger MOG parameter makes it possible for the clouds to exist in the case of the lower background angular velocity. Numerical results are compared with the analytical formula obtained by an asymptotic matching method, and we find that both results are consistent with each other. In particular, it is shown that the larger MOG parameter, the better agreement between analytical and numerical results. This implies that the matching method is a powerful analytical tool to investigate the scalar clouds existing in the Kerr-MOG black holes. Moreover, we obtain the location of the existence lines and show that the clouds are concentrated at the larger radial position for the Kerr-MOG black holes when compared to the Kerr black holes.

We investigate the holographic p-wave superfluid in the background metric of the AdS soliton with RF 2 corrections. Two models, namely, the Maxwell complex vector field model and Yang-Mills theory, are studied in the above context by employing the Sturm-Liouville approach as well as the shooting method. When turning on the spatial components of the gauge field, one observes that, in the probe limit, the inclusion of RF 2 corrections hinders the superfluid phase transition. On the other hand, however, in the absence of the superfluid velocity, it is found that the RF 2 corrections lead to distinct effects for the two models. Regardless of either the RF 2 correction or the spatial component of the gauge field, the phase transition of the system is observed to be always of the second order. Moreover, a linear relationship between the charge density and chemical potential is largely established near the critical point in both holographic superfluid models.

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