Violations of the weak cosmic censorship conjecture in the higher dimensional f(R)f(R) black holes with pressure

We adopt the energy momentum relation of charged particles to study the thermodynamics laws and weak cosmic censorship conjecture of $D$-dimensional $f(R)$ AdS black holes in different phase spaces by considering charged particle absorption. In the normal phase space, it turns out that the laws of thermodynamic and the weak cosmic censorship conjecture are valid. In the extended phase space, though the first law of thermodynamics is valid, the second law of thermodynamics is invalid. More interestingly, the weak cosmic censorship conjecture is shown to be violated only in higher-dimensional near-extremal $f(R)$ AdS black holes. In addition, the magnitudes of the violations for both the second law and weak cosmic censorship conjecture are dependent on the charge $Q$, constant scalar curvature $f'(R_0)$, AdS radius $l$, dimension parameters $p$, and their variations.Comment: Accepted by Eur. Phys. J.

Holographic Einstein rings of Non-commutative black holes

With the help of the AdS/CFT correspondence, we easily derive the desired response function of QFT on the boundary. Using the virtual optical system with a convex lens, we are able to obtain the image of the black hole from the response function and further study the Einstein ring of the non-commutative black holes. All the results show that there are some common features and different features compared to the previous study of other background black holes. The common features include that the holographic ring always appears with the concentric stripe surrounded when the observer located at the north pole, and an extremely bright ring when the observer is at the position of the photon sphere of the black hole. And with the change of the observation position, this ring will change into a luminosity-deformed ring, or light points. In addition to these similarities, there are some different features which are due to the singularity of the event horizon temperature. Explicitly, the relation between temperature and the event horizon $T-z_h$ has two branches when the non-commutative parameter $n$ is fixed. These in turn have an effect on the behavior of the response function and the Einstein ring. For example, the amplitude of the response function $|\langle O\rangle|$ increases with the decrease of the non-commutative strength parameter $n$ for both two branches of $T-n$ relation. However, the amplitude of $|\langle O\rangle|$ increases with the decrease of the temperature $T$ for the left branch of $T-z_h$ relation, while the amplitude of $|\langle O\rangle|$ decreases with the decrease of the temperature $T$ for the right branch. These differences are also reflected in the Einstein ring. Therefore, these differences can be used to distinguish different black hole backgrounds. Furthermore, we show that the non-commutative parameter has an effect on the brightness and the position of Einstein ring.Comment: revised version. arXiv admin note: text overlap with arXiv:2307.01973; text overlap with arXiv:1811.12617, arXiv:1906.09113 by other author

Holographic Einstein Rings of an AdS Black Hole in Massive Gravity

In the context of holography, the Einstein ring of an AdS black hole (BH) in massive gravity (MG) is depicted. An oscillating Gaussian source on one side of the AdS boundary propagates in bulk, and we impose a response function to explain it. Using a wave optics imaging system, we obtain the optical appearance of the Einstein ring. Our research reveals that the ring can change into a luminosity-deformed ring or light spots depending on the variation of parameters and observational positions. When observers are positioned at the north pole, the holographic profiles always appear as a ring with concentric stripe surroundings, and a bright ring appears at the location of the photon sphere of the BH. These findings are consistent with the radius of the photon sphere of the BH, which is calculated in geometrical optics. Our study contributes to a better understanding of the analytical studies of holographic theory, which can be used to evaluate different types of BHs for a fixed wave source and optical system.Comment: 15 pages, 14 figure