In this paper we present a new black hole solution surrounded by dark matter (DM) halo in the galactic center using the mass model of M87 and that coming from the universal rotation curve (URC) dark matter profile representing family of spiral galaxies. In both cases the DM halo density is cored with a size $r_0$ and a central density ${\rho }_0$: $\rho (r)={\rho }_0/(1+r/r_0)(1+(r/r_0{)}^2)$. Since $r_0{\rho }_0=120{\mathrm{M}}_{\odot }/{\mathrm{pc}}^2$ [ Mon. Not. R. Astron. Soc. 397, 1169 (2009)], then by varying the central density one can reproduce the DM profile in any spiral. Using the Newman-Jains method we extend our solution to obtain a rotating black hole surrounded by dark matter halo. We find that the apparent shape of the shadow beside the black hole spin $a$, it also depends on the central density of the surrounded dark matter ${\rho }_0$. As a specific example we consider the galaxy M87, with a central density ${\rho }_0=6.9\times {10}^6{\mathrm{M}}_{\odot }/{\mathrm{kpc}}^3$ and a core radius $r_0=91.2\mathrm{kpc}$. In the case of M87, our analyses show that the effect of dark matter on the size of the black hole shadow is almost negligible compared to the shadow size of the Kerr vacuum solution hence the angular diameter $42\mu \mathrm{as}$ remains almost unaltered when the dark matter is considered. For a small totally dark matter dominated spiral such as UGC 7232, we find similar effect of dark matter on the shadow images compared to the M87. However, in specific conditions having a core radius comparable to the black hole mass and dark matter with very high density, we show that the shadow images decreases compared to the Kerr vacuum black hole. The effect of dark matter on the apparent shadow shape can shed some light in future observations as an indirect way to detect dark matter using the shadow images.

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 noncomplexification 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 $r\to 0$. 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 ${\theta }_0$, 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 ${\theta }_0$. Additionally, we explore the observational implications of $P$ in comparing with the latest Event Horizon Telescope 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.

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 construct a black hole solution surrounded by superfluid dark matter and baryonic matter, and study their effects on the shadow images of the Sgr A $$^{*}$$∗ black hole. To achieve this goal, we have considered two density profiles for the baryonic matter described by the spherical exponential profile and the power law profile including a special case describing a totally dominated dark matter galaxy. Using the present values for the parameters of the superfluid dark matter and baryonic density profiles for the Sgr A $$^{*}$$∗ black hole, we find that the effects of the superfluid dark matter and baryonic matter on the size of shadows are almost negligible compared to the Kerr vacuum black hole. In addition, we find that by increasing the baryonic mass the shadow size increases considerably. This result can be linked to the matter distribution in the galaxy, namely the baryonic matter is mostly located in the galactic center and, therefore, increasing the baryonic matter can affect the size of black hole shadow compared to the totally dominated dark matter galaxy where we observe an increase of the angular diameter of the Sgr A $$^{*}$$∗ black hole of the magnitude $$10^{-5}\,\upmu $$10-5μ arcsec.

As an extension of our previous work [J. Qiao , arXiv:1909.03815.], in this article, we calculate the effects of parity violation on gravitational-wave (GW) waveforms during their propagation in the most general parity-violating gravities, including Chern-Simons modified gravity, ghost-free scalar-tensor gravity, the symmetric teleparallel equivalence of General Relativity theory, Hořava-Lifshitz gravity, and so on. For this purpose, we consider the GWs generated by the coalescence of compact binaries and concentrate on the imprints of the parity violation in the propagation of GWs. With a unified description of GW in the theories of parity-violating gravity, we study the effects of velocity and amplitude birefringence on the GW waveforms. Decomposing the GWs into the circular polarization modes, the two birefringence effects exactly correspond to the modifications in phase and amplitude of GW waveforms, respectively. We find that, for each circular polarization mode, the amplitude, phase, and velocity of GW can be modified by both the parity-violating terms and parity-conserving terms in gravity. Therefore, in order to test the parity symmetry in gravity, we should compare the difference between two circular polarization modes, rather than measure an individual mode. Combining two circular modes, we obtain the GW waveforms in the Fourier domain and obtain the deviations from those in General Relativity. The GW waveforms derived in this paper are also applicable to the theories of parity-conserving gravity, which have the modified dispersion relations (e.g., massive gravity, double special relativity theory, extra-dimensional theories, etc.) or/and have the modified friction terms (e.g., nonlocal gravity, gravitational theory with time-dependent Planck mass, etc.).

The evolutions of the flat Friedmann-Lemaître-Robertson-Walker universe and its linear perturbations are studied systematically in the dressed metric approach of loop quantum cosmology. When it is dominated by the kinetic energy of the inflaton at the quantum bounce, the evolution of the background can be divided into three different phases prior to the preheating: bouncing, transition and slow-roll inflation. During the bouncing phase, the evolution is independent of not only the initial conditions, but also the inflationary potentials. In particular, the expansion factor can be well described by the same exact solution in all the cases considered. In contrast, in the potential-dominated case such a universality is lost. It is because of this universality that the linear perturbations are also independent of the inflationary models and obtained exactly. During the transition phase, the evolutions of the background and its linear perturbations are found explicitly, and then matched to the ones given in the other two phases. Hence, once the initial conditions are imposed, the linear scalar and tensor perturbations will be uniquely determined. Considering two different sets of initial conditions, one imposed during the contracting phase and the other at the bounce, we calculate the Bogoliubov coefficients and find that the two sets yield the same results and all lead to particle creations at the onset of the inflation. Due to the preinflationary dynamics, the scalar and tensor power spectra become scale dependent. By comparing our results with the Planck 2015 data, we find constraints on the total number of $e$-folds since the bounce, in order to be consistent with current observations.