In this paper, we construct an effective rotating loop quantum black hole (LQBH) solution, starting from the spherical symmetric LQBH by applying the Newman-Janis algorithm modified by Azreg-Aïnou's non-complexification procedure, and study the effects of loop quantum gravity (LQG) on its shadow. Given the rotating LQBH, we discuss its horizon, ergosurface, and regularity as r → 0. Depending on the values of the specific angular momentum a and the polymeric function P arising from LQG, we find that the rotating solution we obtained can represent a regular black hole, a regular extreme black hole, or a regular spacetime without horizon (a non-black-hole solution). We also study the effects of LQG and rotation, and show that, in addition to the specific angular momentum, the polymeric function also causes deformations in the size and shape of the black hole shadow. Interestingly, for a given value of a and inclination angle θ0, the apparent size of the shadow monotonically decreases, and the shadow gets more distorted with increasing P . We also consider the effects of P on the deviations from the circularity of the shadow, and find that the deviation from circularity increases with increasing P for fixed values of a and θ0. Additionally, we explore the observational implications of P in comparing with the latest Event Horizon Telescope (EHT) observation of the supermassive black hole, M87*. The connection between the shadow radius and quasinormal modes in the eikonal limit as well as the deflection of massive particles are also considered.

We study primordial gravitational waves (PGWs) in the Horava-Lifshitz (HL) theory of quantum gravity, in which high-order spatial derivative operators, including the ones violating parity, generically appear in order for the theory to be power-counting renormalizable and ultraviolet (UV) complete. Because of both parity violation and non-adiabatic evolution of the modes due to a modified dispersion relationship, a large polarization of PGWs becomes possible, and it could be well within the range of detection of the BB, TB and EB power spectra of the forthcoming cosmic microwave background (CMB) observations.

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 highorder spatial nth derivative terms are always suppressed by a factor ðH=M Ã Þ nÀ2 ðn ! 3Þ, where H denotes the inflationary energy and M Ã 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 ChernSimons 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 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.

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 Diff(M, 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 (UV) and infrared (IR), 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.PACS numbers: 98.80.Cq; 98.80.Bp