We study the strong gravitational lensing effect around rotating black holes in different gravity theories. By calculating the deflection angle of strong gravitational lensing, we evaluate the lensing observables including the image position, separation, magnification, and the time delays between the relativistic images of different rotating black holes. We argue that the differences in image positions, separations between the rotating black hole in modified gravity (MOG) theory and the Kerr black hole in general relativity (GR) are more significant in SgrA* than those in M87*; however the differences in time delays between rotating black holes in MOG and GR are shorter in SgrA* than that in M87*. Our evaluations on lensing observables in the strong gravity regime can help to distinguish the MOG from GR. Furthermore, we investigate the shadow observables of different rotating black holes. Employing the Event Horizon Telescope observations on the angular shadow radius for supermassive M87* and SgrA* black holes, respectively, we estimate the ranges of MOG parameter and obtain its upper limit constraint $0.350\lesssim {\alpha }_{\mathrm{up}}\lesssim 0.485$ and $0.162\lesssim {\alpha }_{\mathrm{up}}\lesssim 0.285$ correspondingly, relating to black hole spins. This is the first constraint on the MOG parameter for rotating supermassive black holes from Event Horizon Telescope observations on the angular shadow radius. Our constraint on the MOG parameter is much tighter compared with the result obtained from the orbital precession of the S2 star.

In this paper we study $3+1$ holographic superconductors with Weyl corrections. We find that the critical temperature of a superconductor with Weyl corrections increases as we amplify the Weyl coupling parameter $\gamma$, indicating the condensation will be harder when the parameter $\gamma$ decreases. We also calculate the conductivity and the ratio of gap frequency over critical temperature $\omega_{g}/T_{c}$ numerically for various coupling parameters. We find that the ratio $\omega_g/T_c$ becomes larger when the Weyl coupling parameter $\gamma$ decreases. We also notice that when $\gamma< 0$ there is an extra spike that appears inside the gap.

In this work we study how entanglement of purification (EoP) and the new quantity of “complexity of purification” are related to each other using theE_P=E_Wconjecture. First, we consider two strips in the same side of a boundary and study the relationships between the entanglement of purification of this mixed state and the parameters of the system such as dimension, temperature, length of the strips and the distance between them. Next, using the same setup, we introduce two definitions for the complexity of mixed states, complexity of purification (CoP) and the interval volume (VI). We study their connections to other parameters similar to the EoP case. Then, we extend our study to more general examples of BTZ black holes solution in massive gravity, charged black holes and multipartite systems. Finally, we give various interpretations of our results using resource theories such as LOCC and also bit thread picture.

In this paper, we analyze the light rays around a static hairy black hole in Horndeski gravity with the use of ray-tracing procedure. We find that a stronger Horndeski hairy parameter corresponds to larger photon sphere as well as critical impact parameter, and wider ranges of photon ring and lensed ring emissions. These influences can be robustly interpreted from the shape of the effective potential of the photon’s radial motion. Based on the distribution of the light rays, we then investigate the optical appearances of the Horndeski hairy black hole surrounded by various thin accretions. First, we consider that the Horndeski hairy black hole is illuminated by the optically and geometrically thin accretion disk. We carefully clarify the contributions from the direct, lensed ring and photon ring intensities to the total observed intensity via the transfer function, which is rarely discussed in this scenario. We find that the Horndeski hair has significant influences on both shadow size and distributions of direct, lensed ring and photon ring brightness in three standard emission profiles. As a result, the rings and images of Horndeski hairy black hole and the origination of their brightness differentiate from those of Schwarzschild black hole (SBH) when viewed in face-on orientation. Then, when the Horndeski hairy black hole is illuminated by thin spherical accretions, the hairy black hole’s shadow surrounded by a bright ring is larger than that of SBH, but the brightness of ring is fainter. Similar to that of SBH, the size of hairy black hole shadow does not change as the radial moving of the spherical accretion, and the brightness for the infalling accretion is fainter than that for the static accretion due to the Doppler effect. Therefore, we argue that the black hole image consisting of the shadow and accretion construction could, in theory, reflect the observational differences between the Horndeski hairy black hole and SBH.

Inspired by the observations of the supermassive black hole M87* by the Event Horizon Telescope (EHT), a remarkable surge in black hole physics is to use the black hole shadow’s observables to distinguish between general relativity and modified theories of gravity, which could also help to reveal the astrophysical nature of the central black hole in the EHT observation. In this paper, we study a charged rotating black hole in conformal gravity, in which the term related to the charge has different falloffs from the usual Kerr-Newman (KN) black hole. We investigate the spacetime properties including the horizons, ergospheres, and photon regions; then, we show the boundary of the black hole shadow and investigate its characteristic observables. These features closely depend on the spin and charge parameters, which are compared with those in Kerr and KN black holes. Then, presupposing that M87* is a charged rotating black hole in conformal gravity, we constrain the black hole parameters via the observational constraints from EHT. We find that the constraints on the inferred circularity deviation ($\mathrm{\Delta }C\lesssim 0.1$) and shadow axial ratio ($1<D_x\lesssim 4/3$) for M87* are satisfied for the entire parameter space of the charged rotating black hole in conformal gravity. However, the shadow angular diameter ${\theta }_d=42\pm 3\mu \mathrm{as}$ gives an upper bound on the parameter space. Our findings indicate that the current charged rotating black hole in conformal gravity could be a candidate for astrophysical black holes. Moreover, the EHT observation of the axial ratio $D_x$ may help us to distinguish between a Kerr black hole and the current charged rotating black hole in conformal gravity in some parameter space.

In this paper, we present the analytic solution for Anti-de Sitter-Nonlinear electrodynamics (AdS-NED) black hole in four dimensions. We study tunneling of vector particles from the AdS-NED black...