Based on the AdS/CFT correspondence, we study the holographic Einstein image of a Gauss–Bonnet AdS black hole in the framework of wave optics. Our results show that for the absolute amplitude of total response function, there always exists the interference pattern when the scalar wave passes through black hole. And, the value of the amplitude depends closely on the properties of Gaussian source and spacetime geometry. More importantly, we also find that the holographic images always appears as a ring surrounded by the concentric stripe when observer located at the north pole. At other positions, this ring will change into a luminosity-deformed ring, or two light points. In addition, the influence of Gauss–Bonnet parameter $$\alpha $$α , wave source and optical system on the holographic image have been carefully addressed and the results show that the radius of ring is dependent of the Gauss–Bonnet parameter $$\alpha $$α but not dependent of wave source and optical system. The holographic images that different types of black holes have different features may shed deep insights on the existence of a gravity dual for a given material.

We investigated the shadows and optical appearances of a new type of regular black holes (BHs) with a Minkowski core under various spherical accretion scenarios. These BHs are constructed by modifying the Newtonian potential based on the minimum observable length in the Generalized Uncertainty Principle (GUP). They correspond one-to-one with traditional regular BHs featuring a de-Sitter (dS) core (such as Bardeen/Hayward BHs), characterized by a quantum gravity effect parameter ( ) and spacetime deformation factor (n). We found that the characteristic parameters give rise to some novel observable features. For these new BHs, both the shadow and photon sphere radii decrease with the increase in , while the observed specific intensity increases. Conversely, as n increases, the shadow and photon sphere radii increase, while the observed specific intensity decreases. Under different spherical accretion scenarios, the shadows and photon sphere radii remain identical; however, the observed specific intensity is greater under static spherical accretion than under infalling spherical accretion. Additionally, we found that these regular BHs with different cores exhibit variations in shadows and optical appearances, particularly under static spherical accretion. Compared with Bardeen BH, the new BHs exhibit a lower observed specific intensity, a dimmer photon ring, and smaller shadow and photon sphere radii. Larger values of lead to more significant differences, and a similar trend was also observed when comparing with Hayward BH. Under infalling spherical accretion, the regular BHs with different cores exhibit only slight differences in observed specific intensity, which become more evident when is relatively large. This suggests that the unique spacetime features of these regular BHs with different cores can be distinguished through astronomical observation.

本文把平直时空中的洛伦兹对称性破缺的Dirac方程推广到动态Vaidya黑洞弯曲时空中. 由于动态Vaidya黑洞的表观视界与类时极限面重合, 根据霍金辐射量子效应理论, 我们在Vaidya黑洞的表观视界r_a = 2M(v)处研究了洛伦兹破缺理论对Dirac粒子Hawking隧穿辐射特征的影响. 我们通过gamma矩阵的对易性质和半经典近似得到了一个新的洛伦兹对称性破缺的Dirac-Hamilton-Jacobi方程, 并利用这一修正的Dirac-Hamilton-Jacobi方程研究了Dirac粒子隧穿辐射的特征, 讨论了洛伦兹对称性破缺对动态球对称Vaidya黑洞的热力学参数的影响. 结果发现, 洛伦兹破缺理论中仅有类以太修正项会对黑洞热力学性质带来修正. 同时, 还发现修正Hawking温度与类以太矢量修正项系数的正负有关, 而我们之前应用洛伦兹破缺理论研究标量粒子的修正Hawking温度也是与类以太矢量修正项系数的正负有关的.

We investigate Joule–Thomson (J–T) expansion process of the regular Ayón Beato–García (ABG) black hole, and compare the J–T expansion process between the regular ABG black hole and the singular AdS black holes. We find that the inversion curves are unclosed and closely related to magnetic monopole charge (MMC) in the black hole solution. The results show that the temperature decreases/increases with the increase of MMC parameter at low/high pressure, in contrast to a branch of the inversion curves for singular AdS black holes. The ratio between the minimum inversion temperature and the critical temperature is also greater than that of any known ratio of singular AdS black holes. In addition, the minimum inversion mass is greater than the minimum mass, so there are some isenthalpic curves without inversion points below the inversion curves, which means that the regular black hole is always in heating process. In contrast of singular charged AdS black holes, the isenthalpic curves cannot exist below the inversion curves, because the event horizon cannot be defined here. Furthermore, we obtain that the minimum inversion mass and the minimum mass depend only on MMC parameter. By fixing the parameters of MMC and the black hole mass, we find that a repulsive core near the origin of the regular black hole may lead to different results from that of the singular AdS black holes in the J–T expansion process.

Superhydrophobic surfaces have attracted much interest for its potential applications. In this study, the superhydrophobic aluminum surfaces were fabricated by method of chemical etching. Aluminum surfaces were firstly chemically etched by hydrochloric acid, and modified with stearic acid. The relationship between the etching time and the surface hydrophobicity was investigated. The contact angle and the sliding angle were tested, the results showed that with increasing etching time, the contact angle experienced a rise and then decrease, while the sliding angle dropped first and then started to climb. A maximum value of 152 degrees for the contact angle and a minimum value of 3 degrees for the sliding angle were obtained with etching time of 1 minute. The results indicated an ideal superhydrophobic property of the aluminum surfaces.

In the tunneling framework, one of us, Jiang, together with Han has studied the black hole spectroscopy via adiabatic invariance, where the adiabatic invariant quantity has been intriguingly obtained by investigating the oscillating velocity of the black hole horizon. In this paper, we attempt to improve Jiang–Han’s proposal in two ways. Firstly, we once again examine the fact that, in different types (Schwarzschild and Painlevé) of coordinates as well as in different gravity frames, the adiabatic invariant \(I_\mathrm{adia} = \oint p_i dq_i\) introduced by Jiang and Han is canonically invariant. Secondly, we attempt to confirm Jiang–Han’s proposal reasonably in more general gravity frames (including Einstein’s gravity, EGB gravity and HL gravity). Concurrently, for improving this proposal, we interestingly find in more general gravity theories that the entropy of the black hole is an adiabatic invariant action variable, but the horizon area is only an adiabatic invariant. In this sense, we emphasize the concept that the quantum of the black hole entropy is more natural than that of the horizon area.