Maxwell perturbations on asymptotically Anti-de-Sitter spacetimes: generic boundary conditions and a new branch of quasinormal modes

Perturbations of asymptotically Anti-de-Sitter (AdS) spacetimes are often considered by imposing field vanishing boundary conditions (BCs) at the AdS boundary. Such BCs, of Dirichlet-type, imply a vanishing energy flux at the boundary, but the converse is, generically, not true. Regarding AdS as a gravitational box, we consider vanishing energy flux (VEF) BCs as a more fundamental physical requirement and we show that these BCs can lead to a new branch of modes. As a concrete example, we consider Maxwell perturbations on Kerr-AdS black holes in the Teukolsky formalism, but our formulation applies also for other spin fields. Imposing VEF BCs, we find a set of two Robin BCs, even for Schwarzschild-AdS black holes. The Robin BCs on the Teukolsky variables can be used to study quasinormal modes, superradiant instabilities and vector clouds. As a first application, we consider here the quasinormal modes of Schwarzschild-AdS black holes. We find that one of the Robin BCs yields the quasinormal spectrum reported in the literature, while the other one unveils a new branch for the quasinormal spectrum.

Critical magnetic elds in superconducting systems with semi-metallic bands

In this work, we study the Zeeman splitting effects in the parallel magnetic field versus temperature phase diagram of two-dimensional superconductors with one graphene-like band and the orbital effects of perpendicular magnetic fields in isotropic two-dimensional semi-metallic superconductors. We show that when parallel magnetic fields are applied to graphene and as the intraband interaction decreases to a critical value, the width of the metastability region present in the phase diagram decreases, vanishing completely at that critical value. In the case of two-band superconductors with one graphene-like band, a new critical interaction, associated primarily with the graphene-like band, is required in order for a second metastability region to be present in the phase diagram. For intermediate values of this interaction, a low-temperature first-order transition line bifurcates at an intermediate temperature into a first-order transition between superconducting phases and a second-order transition line between the normal and the superconducting states. In our study on the upper critical fields in generic semi-metallic superconductors, we find that the pair propagator decays faster than that of a superconductor with a metallic band. As result, the zero field band gap equation does not have solution for weak intraband interactions, meaning that there is a critical intraband interaction value in order for a superconducting phase to be present in semi-metallic superconductors. Finally, we show that the out-of-plane critical magnetic field versus temperature phase diagram displays a positive curvature, contrasting with the parabolic-like behaviour typical of metallic superconductors.