In this paper, we study the shadow cast by two types of charged and slowly rotating black holes in the Einstein-Æther theory of gravity. These two types of black holes correspond to two specific combinations of the coupling constants of the æther field, i.e., $c_{14}=0$ but $c_{123}\ne 0$ for the first type and $c_{123}=0$ for the second type. For both types of black holes, in addition to the mass and charge of the black holes, we show that the presence of the æther field can also affect the size of the shadow. For the first type of black hole, it is shown that the shadow size increases with the parameter $c_{13}$, while for the second type of black hole, the shadow size still increases with $c_{13}$ but decreases with the parameter $c_{14}$. With these properties of the æther parameters, we also discuss the observational constraints on these parameters by using the data of the first black hole image by the Event Horizon Telescope. In addition, we also explore the effect of the æther field on the deflection angle of light and the time delay by using the Gauss-Bonnet theorem. It is shown that, for a specific combination $c_{123}=0$, the deflection angle/time delay is slightly affected by the æther parameter $c_{13}$ at the leading order.

In this paper, we obtain an effective metric describing a regular and rotating magnetic black hole (BH) solution with a Yang-Mills electromagnetic source in Einstein-Yang-Mills (EYM) theory using the Newman-Janis (NJ) algorithm via the noncomplexification radial coordinate procedure. We then study the BH shadow and the quasinormal modes (QNMs) for massless scalar and electromagnetic fields and the quasiperiodic oscillations (QPOs). To this end, we also study the embedding diagram for the rotating EYM BH. The energy conditions, shadow curvature radius, topology, and the dynamical evolution of scalar and electromagnetic perturbations using the time domain integration method are investigated. We show that the shadow radius decreases by increasing the magnetic charge, while the real part of QNMs of scalar and electromagnetic fields increases by increasing the magnetic charge. This result is consistent with the inverse relation between the shadow radius and the real part of QNMs. In addition, we have studied observational constraints on the EYM parameter $\lambda$ via frequency analysis of QPOs and the EHT data of shadow cast by the M87 central black hole. We also find that the decaying rate of the EYM BH is slower than that of the neutral and ends up with a tail. We argue that the rotating EYM black hole can be distinguished from the Kerr-Newman black hole with a magnetic charge based on the difference between the angular diameters of their shadows.

In this paper, we investigate the effects of a dark matter (DM) spike on the neighborhood of Sgr A*, the black hole (BH) in the center of the Milky Way. Our main goal is to investigate whether current and future astronomical observations of Sgr A* could detect the presence of such a DM spike. At first, we construct the spacetime metric around a static and spherically symmetric BH with a DM spike, and later, this solution is generalized for a rotating BH using the Newman–Janis–Azreg-Aïnou algorithm. For the static BH metric, we use the data of the S2 star orbiting Sgr A* to determine and analyze the constraints on the two free parameters characterizing the density and innermost boundary of the DM halo surrounding the BH. Furthermore, by making use of the available observational data for the DM spike density ρ _sp and the DM spike radius R _sp in the Milky Way, we consider a geometrically thick accretion disk model around the Sgr A* BH and demonstrate that the effect of DM distribution on the shadow radius and the image of the BH is considerably weak for realistic DM densities, becoming significant only when the DM density is of the order ρ _sp ∼ (10⁻¹⁹–10⁻²⁰) g cm⁻³ near the BH. We further analyze the possibility of observing this effect with radio interferometry, simulating observations with an EHT-like array, and find that it is unlikely to be detectable in the near future.

In this paper, we study the effects of parity violation on non-Gaussianities of primordial gravitational waves in the framework of the Hořava-Lifshitz theory of gravity, in which high-order spatial derivative operators, including the ones violating parity, generically appear. By calculating the three-point function, we find that the leading-order contributions to the non-Gaussianities come from the usual second-order derivative terms, which produce the same bispectrum as that found in general relativity. The contributions from high-order spatial $n$th derivative terms are always suppressed by a factor $(H/M_{*}{)}^{n-2}(n\ge 3)$, where $H$ denotes the inflationary energy and $M_{*}$ the suppression mass scale of the high-order spatial derivative operators of the theory. Therefore, the next leading-order contributions come from the three-dimensional gravitational Chern-Simons term. With some reasonable arguments, it is shown that this three-dimensional operator is the only one that violates the parity and in the meantime has nonvanishing contributions to non-Gaussianities.

In this paper, we use a suitable conformal rescaling to construct static and rotating regular black holes in conformal massive gravity. The new metric is characterized by the mass $M$, the “scalar charge” $Q$, the angular momentum parameter $a$, the “hair parameter” $\lambda$, and the conformal scale factor encoded in the parameter $L$. We explore the shadow images and the deflection angles of relativistic massive particles in the spacetime geometry of a rotating regular black hole. For $\lambda \ne 0$ and $Q>0$, the shadow is larger than the shadow of a Kerr black hole. In particular, if $\lambda <0$, the shadow radius increases considerably. For $\lambda \ne 0$ and $Q<0$, the shadow is smaller than the shadow of a Kerr black hole. Additionally, we put observational constraints on the parameter $Q$ using the latest Event Horizon Telescope observation of the supermassive black hole M87*. Lastly, using the Gauss-Bonnet theorem, we show that the deflection angle of massive particles is strongly affected by the parameter $L$. The deflection angle might be used to distinguish rotating regular black holes from rotating singular black holes.

We consider an extended theory of Horava-Lifshitz gravity with the detailed balance condition softly breaking, but without the projectability condition. With the former, the number of independent coupling constants is significantly reduced. With the latter and by extending the original foliation-preserving diffeomorphism symmetry $\mathrm{Diff}(M,\mathcal{F})$ to include a local $U(1)$ symmetry, the spin-0 gravitons are eliminated. Thus, all the problems related to them disappear, including the instability, strong coupling, and different speeds in the gravitational sector. When the theory couples to a scalar field, we find that the scalar field is not only stable in both the ultraviolet and infrared, but also free of the strong coupling problem, because of the presence of high-order spatial derivative terms of the scalar field. Furthermore, applying the theory to cosmology, we find that due to the additional $U(1)$ symmetry, the Friedmann-Robertson-Walker (FRW) universe is necessarily flat. We also investigate the scalar, vector, and tensor perturbations of the flat FRW universe, and derive the general linearized field equations for each kind of the perturbations.