In this paper, we first analyze the horizon structure of the acoustic charged black hole in curved spacetime and then study its acoustic shadow as well as the near-horizon characteristics including the quasinormal mode (QNM) frequencies and analog Hawking radiation. We find that the radius of the acoustic shadow for an acoustic charged black hole is larger than that for a Reissner-Nordström (RN) black hole, and both of them are suppressed by increasing the black hole charge because their related outer horizons become smaller. Then the QNM frequencies under scalar field perturbation and its eikonal limit are computed via numeric method and acoustic shadow, respectively. We find that the acoustic charged black hole is stable under the perturbation and the QNM frequencies are much weaker than that for the astrophysical black hole. Moreover, as the tuning parameter increases, the perturbation oscillates more mildly and its damping time becomes longer, while as the charge increases, the oscillation is enhanced slightly and the perturbation decays a little faster which is different from that in a RN black hole. Finally, we numerically study the analog Hawking radiation. We find that the gray-body factor and energy emission rate are suppressed by the angular number and the charge, but they do not monotonically depend on the tuning parameter in the acoustic charged black hole. The behavior of the energy emission rate affected by the parameters could be explained by the dependent behavior of the Hawking temperature. We expect that our results could shed light to the study of black holes in both theoretical and experimental perspectives.

We holographically investigate the scalarization in the Einstein-scalar-Gauss-Bonnet gravity with a negative cosmological constant. We find that instability exists for both Schwarzschild-AdS (anti–de Sitter) and Reissner-Nordström-AdS black holes with planar horizons when we have proper interactions between the scalar field and the Gauss-Bonnet curvature corrections. We relate such instability to possible holographic scalarization and construct the corresponding hairy black hole solutions in the presence of the cosmological constant. Employing the holographic principle, we expect that such bulk scalarization corresponds to the boundary description of the scalar hair condensation without breaking any symmetry, and we calculate the related holographic entanglement entropy of the system. Moreover, we compare the mechanisms of the holographic scalarizations caused by the effect of the coupling of the scalar field to the Gauss-Bonnet term and holographic superconductor effect in the presence of an electromagnetic field, and unveil their differences in the effective mass of the scalar field, the temperature-dependent property, and the optical conductivity.

Various properties of acoustic black holes constructed in Minkowski spacetime have been widely studied in the past decades. Recently the acoustic black holes in general spacetime were proposed. In this paper, we first investigate the basic characteristics of “curved” acoustic black holes in Schwarzschild spacetime, including the quasinormal modes, grey-body factor, and analogous Hawking radiation. We find that the signal of the quasinormal mode is weaker than that of the Schwarzschild black hole. Moreover, as the tuning parameter increases, both the positive real part and negative imaginal part of the quasinormal frequency approach to the horizonal axis, but they will not change sign. This means that all the perturbations could die off and the system is stable under those perturbations. Since the larger tuning parameter suppresses the effective potential barrier, so it enhances the grey-body factor. The energy emission rate of Hawking radiation does not monotonically increase the tuning parameter because of the nonmonotonicity of the Hawking temperature. Finally, as a first attempt, we study the acoustic black hole shadow. The radius of the acoustic shadow becomes larger as the tuning parameter increases because both the related acoustic horizon and the acoustic sphere become larger. Our studies could help us to further understand the near horizon geometrical features of the black hole. We also expect that our observations could be detected experimentally in the near future.

We examine the strong cosmic censorship in the Reissner–Nordstrom–de Sitter (RN-dS) black hole by investigating the evolution of a scalar field non-minimally coupled to the curvature. We find that for the stable RN-dS black hole, with the increase of the coupling parameter, the violation of the strong cosmic censorship occurs at a larger critical charge ratio. But such an increase of the critical charge is suppressed by the increase of the cosmological constant. Different from the minimal coupling situation, it is possible to accommodate $$\beta \ge 1$$β≥1 in the near extremal black hole when the scalar field is non-minimally coupled to curvature. $$\beta $$β here is defined as $$\beta \equiv -\frac{\mathrm {Im}\;\omega }{\kappa _{-}}$$β≡-Imωκ- where $$\kappa _{-}$$κ- is the surface gravity of Cauchy horizon and $$\omega $$ω is the frequency of quasinormal modes. The increase of the cosmological constant can allow $$\beta \ge 1$$β≥1 to be satisfied for even smaller value of the coupling parameter. The existence of $$\beta \ge 1$$β≥1 implies that the resulting curvature can continuously cross the Cauchy horizon.

We investigate the frame-dragging effect of the hairy Kerr spacetimes on the spin of a test gyro and accretion disk. First, we analyze Lense-Thirring (LT) precession frequency, geodetic precession frequency, and the general spin precession frequency of a test gyro attached to a stationary observer in the spacetime. We find that the black hole hair suppresses those precession frequencies in comparison with that which occurs in Kerr spacetime in general relativity. Moreover, using those frequencies as a probe, we differentiate the hairy Kerr black hole (BH) from naked singularity (NS). Specifically, as the observer approaches the central source along any direction, the frequencies grow sharply for the hairy Kerr BH, while for the hairy NS they are finite except at the ring singularity. Then, we investigate the quasiperiodic oscillations (QPOs) phenomena as the accretion disk approaches the hairy Kerr BH or NS. To this end, we analyze the bound circular orbits and their perturbations. We find that as the orbits approach the corresponding innermost stable circular orbit (ISCO), both LT precession frequency and periastron precession frequency behave differently in the hairy Kerr BH and NS. Additionally, the hairy parameters have significant effects on the two frequencies. We expect that our theoretical studies could shed light on astrophysical observations in distinguishing hairy theories from Einstein’s gravity, and also in distinguishing BH from NS in spacetime with hair.

Black hole spontaneous scalarization has been attracting more and more attention as it circumvents the well-known no-hair theorems. In this work, we study the scalarization in Einstein–scalar-Gauss–Bonnet theory with a probe scalar field in a black hole background with different curvatures. We first probe the signal of black hole scalarization with positive curvature in different spacetimes. The scalar field in AdS spacetime could be formed easier than that in flat case. Then, we investigate the scalar field around AdS black holes with negative and zero curvatures. Comparing with negative and zero cases, the scalar field near AdS black hole with positive curvature could be much easier to emerge. And in negative curvature case, the scalar field is the most difficult to be bounded near the horizon.