It has been shown that the mass of a charged scalar field in the background of a charged stringy black hole is never able to generate a potential well outside the event horizon to trap the superradiant modes. This is to say that the charged stringy black hole is stable against massive charged scalar perturbations. In this paper we will study the superradiant instability of the massless scalar field in the background of charged stringy black hole due to a mirror-like boundary condition. The analytical expression of the frequencies of unstable superradiant modes is derived by using the asymptotic matching method. It is also pointed out that the black hole mirror system becomes extremely unstable for a large charge q of the scalar field and a small mirror radius r m .

We numerically study the superradiant instability of charged massless scalar field in the background of charged stringy black hole with mirror-like boundary condition. We compare the numerical result with the previous analytical result and show the dependencies of this instability upon various values of black hole charge Q , scalar field charge q, and mirror radius r m . Especially, we have observed that imaginary part of BQN frequencies grows with the scalar field charge q rapidly.

It has been proved that the charged stringy black holes are stable under the perturbations of massive charged scalar fields. However, superradiant instability can be generated by adding the mirror-like boundary condition to the composed system of charged stringy black hole and scalar field. The unstable boxed quasinormal modes have been calculated by using both analytical and numerical method. In this paper, we further provide a time domain analysis by performing a long time evolution of charged scalar field configuration in the background of the charged stringy black hole with the mirror-like boundary condition imposed. We have used the ingoing Eddington-Finkelstein coordinates to derive the evolution equation, and adopted Pseudo-spectral method and the forth-order Runge-Kutta method to evolve the scalar field with the initial Gaussian wave packet. It is shown by our numerical scheme that Fourier transforming the evolution data coincides well with the unstable modes computed from frequency domain analysis. The existence of the rapid growth mode makes the charged stringy black hole a good test ground to study the nonlinear development of superradiant instability.

It was reported that massive scalar fields can form bound states around Kerr black holes (Herdeiro and Radu, Phys. Rev. Lett. 112:221101, 2014). These bound states are called scalar clouds; they have a real frequency ω = m H , where m is the azimuthal index and H is the horizon angular velocity of Kerr black hole. In this paper, we study scalar clouds in a spherically symmetric background, i.e. charged stringy black holes, with the mirror-like boundary condition. These bound states satisfy the superradiant critical frequency condition ω = q H for a charged scalar field, where q is the charge of the scalar field, and H is the horizon's electrostatic potential. We show that, for the specific set of black hole and scalar field parameters, the clouds are only possible for specific mirror locations r m . It is shown that analytical results of the mirror location r m for the clouds perfectly coincide with numerical results in the q Q 1 regime. We also show that the scalar clouds are also possible when the mirror locations are close to the horizon. Finally, we provide an analytical calculation of the specific mirror locations r m for the scalar clouds in the q Q 1 regime.

We study a holographic model which exhibits a quantum phase transition from the strongly interacting Weyl semimetal phase to an insulating phase. In the holographic insulating phase there is a hard gap in the real part of frequency dependent diagonal conductivities. However, the anomalous Hall conductivity is nonzero at zero frequency, indicting that it is a Chern insulator. This holographic quantum phase transition is always of first order, signified by a discontinuous anomalous Hall conductivity at the phase transition, in contrast to the very continuous holographic Weyl semimetal/trivial semimetal phase transition. Our work reveals the novel phase structure of strongly interacting Weyl semimetal.. The independent parameters are T, f 1 , h 1 , A z1 , φ 1 . With the above scaling symmetries, we only have two free parameters, which correspond to M/b, T /b in the dual field theory.