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Abstract The global monopole solutions which give rise to quite unusual physical phenomena have captured considerable attention. In this paper, we study the Einstein ring of the spherically symmetric AdS black hole solution with a global monopole based on the AdS/CFT correspondence. With the help of the given response function of the QFT on the boundary, we construct the holographic images of the black hole in the bulk. Our results exhibit the absolute amplitude of total response function $$|\langle \mathcal {O}\rangle |$$ | ⟨ O ⟩ | increases with the decrease of the monopole parameter b and the temperature T. And the frequency $$\omega $$ ω of the Gaussian source will also increase the absolute amplitude. These parameters also affects the Einstein ring. With the change of the observation position, this ring will change from the concentric stripe to a luminosity-deformed ring, or light points. And the monopole parameter has an effect on the brightness and the position of Einstein ring. All these results imply that the holographic images can be used as an effective tool to distinguish different types of black holes for fixed wave source and optical system. These theoretical proposal opens a door to gravitational phenomena on strongly correlated material. Therefore, the holographic Einstein ring is of great theoretical and experimental significance for our research. In theory, it provides us a new way to find a necessary condition for the existence of the dual black hole. And experimentally speaking, if we can realize suitable targets for observing AdS black holes successfully, we would be able to observe Einstein rings by tabletop experiments when we apply localized sources on such materials and measure their responses.

Abstract With the help of AdS/CFT correspondence, we derive the desired response function of QFT on the boundary of the non-commutative black hole. Using the virtual optical system with a convex lens, we obtain the Einstein rings of the black hole from the response function. All the results show that the holographic ring always appears with the concentric stripe when the observer located at the north pole. With the change of the observation position, the ring changes into a luminosity-deformed ring, or bright spot. We also investigate the effect of the non-commutative parameter on the ring and find the ring radius becomes larger as the parameter increases. The effect of the temperature on the ring radius is also investigated, it is found that the higher the temperature, the smaller the ring radius. In addition, we also obtain the ingoing angle of the photon via geometric optics, as expected, this angle is consistent well with the angle of the Einstein ring obtained via holography.

Under the help of AdS/CFT correspondence, the Einstein ring of a charged black hole in conformal gravity has been studied. As an alternative to standard Einstein’s theory, the conformal gravity is both renormalizable and unitary. And such conformal theory can naturally solve some troublesome problems in physics, such as the quantum gravity problem, the dark matter problem and so on. Considering the conformal gravity has many advantages, therefore in this paper, we study Einstein ring and the effect of gravity-related parameters c0, temperature T and chemical potential u on such Einstein ring in the conformal gravity through the holographic method. Explicitly, imposing an oscillating Gauss source on one side of the AdS boundary which propagates in the bulk, the response functions are derived on the other side of the boundary. Given the proposed wave optics system, the Einstein rings are observed as expected. All these results reveal that when the observer locates at the north pole, there always exists the Einstein ring and surrounding concentric stripes. And such ring becomes into a luminosity-deformed ring or light spot while the observer departs away from the north pole. We also investigate the effect of temperature T, chemical potential u and gravity-related parameters c0 on the ring radius. We find the ring radius increases with the decrease of the temperature, increase of the chemical potential, and increase of the gravity-related parameters respectively. And more, in conformal gravity, because the charge does not appear in the metric but is given by the constraint relation, the chemical potential affects the radius of the ring differently compared with that in Einstein’s gravity. To check the results in the framework of holography, we investigate the ingoing angle of photon at the photon ring via geometric optics and find it is consistent with the angle of Einstein ring obtained via holography.

Background: Semantic segmentation is crucial in medical image diagnosis. Traditional deep convolutional neural networks excel in image classification and object detection but fall short in segmentation tasks. Enhancing the accuracy and efficiency of detecting high-level cervical lesions and invasive cancer poses a primary challenge in segmentation model development. Methods: Between 2018 and 2022, we retrospectively studied a total of 777 patients, comprising 339 patients with high-level cervical lesions and 313 patients with microinvasive or invasive cervical cancer. Overall, 1554 colposcopic images were put into the DeepLabv3+ model for learning. Accuracy, Precision, Specificity, and mIoU were employed to evaluate the performance of the model in the prediction of cervical high-level lesions and cancer. Results: Experiments showed that our segmentation model had better diagnosis efficiency than colposcopic experts and other artificial intelligence models, and reached Accuracy of 93.29 %, Precision of 87.2 %, Specificity of 90.1 %, and mIoU of 80.27 %, respectively. Conclution: The DeepLabv3+ model had good performance in the segmentation of cervical lesions in colposcopic post-acetic-acid images and can better assist colposcopists in improving the diagnosis.

The Van der Waals-like phase transition is observed in temperature–thermal entropy plane in spherically symmetric charged Gauss–Bonnet–AdS black hole background. In terms of AdS/CFT, the non-local observables such as holographic entanglement entropy, Wilson loop, and two point correlation function of very heavy operators in the field theory dual to spherically symmetric charged Gauss–Bonnet–AdS black hole have been investigated. All of them exhibit the Van der Waals-like phase transition for a fixed charge parameter or Gauss–Bonnet parameter in such gravity background. Further, with choosing various values of charge or Gauss–Bonnet parameter, the equal area law and the critical exponent of the heat capacity are found to be consistent with phase structures in temperature–thermal entropy plane.

Phase structure of the quintessence Reissner–Nordström–AdS black hole is probed by the nonlocal observables such as holographic entanglement entropy and two point correlation function. Our result shows that, as the case of the thermal entropy, both the observables exhibit the Van der Waals-like phase transition. To reinforce this conclusion, we further check the equal area law for the first order phase transition and critical exponent of the heat capacity for the second order phase transition. We also discuss the effect of the state parameter on the phase structure of the nonlocal observables.

The phase structure of holographic entanglement entropy is studied in massive gravity for the quantum systems with finite and infinite volumes, which in the bulk is dual to calculating the minimal surface area for a black hole and black brane respectively. In the entanglement entropy–temperature plane, we find for both the black hole and black brane there is a Van der Waals-like phase transition as the case in thermal entropy–temperature plane. That is, there is a first order phase transition for the small charge and a second order phase transition at the critical charge. For the first order phase transition, the equal area law is checked and for the second order phase transition, the critical exponent of the heat capacity is obtained. All the results show that the phase structure of holographic entanglement entropy is the same as that of thermal entropy regardless of the volume of the spacetime on the boundary.

In a recent paper, arXiv:1309.4877, a holographic p-wave model has been proposed in an Einstein–Maxwell-complex vector field theory with a negative cosmological constant. The model exhibits rich phase structure depending on the mass and the charge of the vector field. We investigate the behavior of the entanglement entropy of dual field theory in this model. When the above two model parameters change, we observe the second order, first order and zeroth order phase transitions from the behavior of the entanglement entropy at some intermediate temperatures. These imply that the entanglement entropy can indicate not only the occurrence of the phase transition, but also the order of the phase transition. The entanglement entropy is indeed a good probe to phase transition. Furthermore, the “retrograde condensation” which is a sub-dominated phase is also reflected on the entanglement entropy.

From the viewpoint of holography, the phase structure of a 5-dimensional Reissner-Nordström-AdS black hole is probed by the two-point correlation function, Wilson loop, and entanglement entropy. As the case of thermal entropy, we find for all the probes that the black hole undergoes a Hawking-Page phase transition, a first-order phase transition, and a second-order phase transition successively before it reaches a stable phase. In addition, for these probes, we find that the equal area law for the first-order phase transition is valid always and the critical exponent of the heat capacity for the second-order phase transition coincides with that of the mean field theory regardless of the size of the boundary region.

Loop quantum cosmology (LQC) is very powerful to deal with the behavior of early universe. Moreover, the effective loop quantum cosmology gives a successful description of the universe in the semiclassical region. We consider the apparent horizon of the Friedmann-Robertson-Walker universe as a thermodynamical system and investigate the thermodynamics of LQC in the semiclassical region. The effective density and effective pressure in the modified Friedmann equation from LQC not only determine the evolution of the universe in LQC scenario but also are actually found to be the thermodynamic quantities. This result comes from the energy definition in cosmology (the Misner-Sharp gravitational energy) and is consistent with thermodynamic laws. We prove that within the framework of loop quantum cosmology, the elementary equation of equilibrium thermodynamics is still valid.