In this paper, under the illumination of thin disk accretion, we have employed the ray-tracing method to carefully investigate shadows and rings of the Kehagias-Sfetsos(KS) black hole in deformed Hořava-Lifshitz(HL) gravity. The results show that the event horizon r₊, the radius r_p and impact parameter b_p of photon sphere are all decreased with the increase of the HL parameter ω, but the effective potential increases. And, it also turns out that the trajectories of light rays emitted from the north pole direction are defined as the direct emission, lensing ring and photon ring of KS black hole, on the basis of orbits n = ϕ/2π. As black hole surrounded by thin disk accretion, we show that the corresponding transfer functions have their values increased with the parameter ω. More importantly, we also find that the direct emissions always dominate the total observed intensity, while lensing rings as a thin ring make a very small contribution and photon ring as a extremely narrow ring make a negligible contribution, for all three toy-model functions. In view of this, the results finally imply that shadows and rings as the observational appearance of KS black hole exhibit some obvious interesting features, which might be regarded as an effective way to distinguish black holes in HL gravity from the Schwarzschild black hole.

In this paper, we explore three simple models of accretions on a global monopole black hole in f(R) theory, and numerically study the corresponding observational appearances as seen by an observer located at the asymptotic infinity and the certain region out of black hole. For the thin-disk accretion, the results here show that the brighter lensing ring and the darker photon ring that around black hole shadow, always make a small contribution and a negligible contribution to total observed intensity respectively. While, the direct emission of disk contributes a dominant part, and the size of shadow always depends on the disk’s location. For the static and infalling spherical accretions, it turns out that the radiuses of the shadows and photon spheres are always same for both accretions, which implies that the boundary of shadow represents the signature of the spacetime geometry in this case. However, we also find that the brightness of shadow in infalling accretion is darker than that in static case since the Doppler effect is taken into account. In addition, the effect of the global monopole parameter $$\eta $$η and f(R) parameter $$\psi _0$$ψ 0 on observational appearances of black hole are clearly emphasized throughout of this paper. Finally, we conclude that black hole shadows and the related rings with some different observable features can be used for us to distinguish black holes from different gravity theories and set the upper limits to the f(R) parameter $$\psi _0$$ψ 0 .

Taking the quantum electrodynamics (QED) effect into account, we investigate the geometrical-optics appearance of the Euler–Heisenberg (EH) black hole (BH) under the different accretion flows context, which depends on the BH space-time structure and different sources of light. The more significant magnetic charge leads to the smaller shadow radius for the EH BH, while the different values of the EH parameter do not ruin it. Different features of the corresponding two-dimensional shadow images are derived for the three optically thin accretion flow models. It is shown that the total observed intensity in the static spherical accretion flow scenario leads than that of the infalling spherical accretion flow under same parameters, but the size and position of the EH BH shadows do not change in both of these accretions flows, implying that the BH shadow size depends on the geometric space-time and the shadows luminosities rely on the accretion flow morphology. Of particular interest is that a thin disk accretion model illuminated the BH, we found that the contribution of the lensing ring to the total observed flux is less than $$5\%$$5 % , and the photon ring is less than $$2\%$$2 % , indicating that the direct emission dominates the optical appearance of the EH BH. It is also believed that the optical appearance of the BH image depends on the accretion disk radiation position in this scenario, which can serve as a probe for the disk structure around the active galactic nucleus (AGN) of M87 $$^{*}$$∗ like.

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.

Considering a charged black hole (BH) surrounded by a perfect fluid radiation field (PFRF) in Rastall gravity, we investigate this BH shadow and photon sphere on different spherical accretions backgrounds. The effect of the PFRF parameter/BH charge on the critical impact parameter is studied by investigating the light deflection near this BH. The luminosity of these BH shadows in different spherical accretions is obtained, respectively. It is found that the shadow of this BH with infalling spherical accretion is darker than static spherical accretion, and the photon sphere with infalling spherical accretion is brighter than a static one. We creatively investigate the effects of the BH charge/PFRF parameter on the luminosity of BH shadow and photon sphere. The results implying that the BH shadow is a signature of space-time geometry, and the photon sphere luminosity is affected by accretion materials and BH itself.