Qi-Ming Fu

As is well-known, black hole plays an important role in probing the quantum effects of gravity in the strong-field regime. In this paper, we focus on a polymerized black hole and investigate the quantum effects on the redshift, blueshift and gravitational redshift of photons emitted by massive particles revolving around this black hole. With a general relativistic formalism, we obtain two elegant and concise expressions for the mass of the black hole and the quantum parameter in terms of few direct observables, and find that all the frequency shifts of photons decrease with the quantum parameter. By expanding the total frequency shift for large orbit of the emitter, low peculiar redshift, and small azimuthal angle, we find that the leading contributions to the frequency shift are originated from the kinematic shift and peculiar shift, and the quantum effects make a negligible contribution. In addition, we study the effects of the plasma on the redshift/blueshift for the first time, and conclude that the presence of plasma results in the decrease of the redshift/blueshift.

As is well-known, black hole plays an important role in probing the quantum effects of gravity in the strong-field regime. In this paper, we focus on a polymerized black hole and investigate the quantum effects on the redshift, blueshift, and gravitational redshift of photons emitted by massive particles revolving around this black hole. With a general relativistic formalism, we obtain two elegant and concise expressions for the mass of the black hole and the quantum parameter in terms of few direct observables, and find that all the frequency shifts of photons decrease with the quantum parameter. By expanding the total frequency shift for large orbit of the emitter, low peculiar redshift, and small azimuthal angle, we find that the leading contributions to the frequency shift are originated from the kinematic shift and peculiar shift, and the quantum effects make a negligible contribution. In addition, we study the effects of the plasma on the redshift/blueshift for the first time, and conclude that the presence of plasma results in the decrease of the redshift/blueshift.

Black hole shadow and gravitational lensing play important roles in testing gravitational theories in the strong field regime. As the first-order modifications from quantum gravity, the nonlocality can be manifested by black hole shadow and gravitational lensing. For example, the cut-off parameter introduced by nonlocality will affect the shape and size of the black hole shadow, and also affect the deflection angle of light rays. In this paper, we mainly investigate the effects of the nonlocality on the black hole shadow and the gravitational lensing for two types of rotating black holes in nonlocal gravity. It is found that the size of the black hole shadow decreases with the cut-off parameter since the nonlocality weakens the gravitational constant, and the shape of the shadow gets more deformed with the increase of the cut-off parameter. However, if the rotation parameter is small, the shape of the shadow is almost a circle even though the cut-off parameter approaches its maximum. The energy emission rate in both models is also studied. The results show that there is a peak for each curve and the peak decreases and shifts to the low frequency with the increase of the cut-off parameter. Besides, we also explore the shadow of both types of black holes surrounded by a nonmagnetized pressureless plasma which satisfies the separability condition. It is found that the plasma has a frequency-dependent dispersive effect on the size and shape of the black hole shadow. For the gravitational lensing, we find that the cut-off parameter of model A makes a positive contribution to the deflection angle, which can be compared with the contribution of the rotation parameter, while the cut-off parameter of model B makes a negative contribution which can be ignored. These results may be helpful for probing nonlocal gravity in future observations.

Black hole shadow and gravitational lensing play important roles in testing gravitational theories in the strong field regime. As the first-order modifications from quantum gravity, the nonlocality can be manifested by black hole shadow and gravitational lensing. For example, the nonlocal parameter introduced by nonlocality will affect the shape and size of the black hole shadow, and also affect the deflection angle of light rays. In this paper, we mainly investigate the effects of the nonlocality on the black hole shadow and the gravitational lensing for two types of rotating black holes in nonlocal gravity. It is found that the size of the black hole shadow decreases with the nonlocal parameter since the nonlocality weakens the gravitational constant, and the shape of the shadow becomes more deformed with the increase in the nonlocal parameter. However, if the rotation parameter is small, the shape of the shadow is almost a circle even though the nonlocal parameter approaches its maximum. The energy emission rate in both models is also studied. The results show that there is a peak for each curve and the peak decreases and shifts to the low frequency with the increase in the nonlocal parameter. In addition, we also explore the shadow of both types of black holes surrounded by a nonmagnetized pressureless plasma which satisfies the separability condition. It is found that the plasma has a frequency-dependent dispersive effect on the size and shape of the black hole shadow. For the gravitational lensing, we find that the nonlocal parameter of model A makes a positive contribution to the deflection angle, which can be compared with the contribution of the rotation parameter, while the nonlocal parameter of model B makes a negative contribution which can be ignored. These results may be helpful for probing nonlocal gravity in future observations.

It is well known that general relativity is an effective theory of gravity at low energy scale, and actually quantum effects cannot be ignored in the strong-field regime. As a strong gravitational object, a black hole plays a key role in testing the quantum effects of gravity in the strong-field regime. In this paper, we focus on the black hole in effective loop quantum gravity and investigate what the influences are of the quantum effects on the weak and strong bending angles of light rays. We find that this black hole could be a Schwarzschild black hole, a regular black hole, a one-way traversable wormhole, or a two-way traversable wormhole for the different values of the quantum parameter, and the strong bending angle for this compact object exhibits two different divergent behaviors, i.e., the logarithmic divergence and nonlogarithmic divergence. There is a series of relativistic images on both sides of the optical axis. Only the outermost one can be resolved as a single image, and all others are packed together at the limiting angular position. It is interesting to note that the angular separation between the outermost relativistic image and the others initially increases and then decreases as the quantum parameter increases, indicating that there is a maximum in the angular separation. The maximum is reached after the black hole becomes a wormhole, which can be taken as a signal for the formation of the wormhole. Moreover, the limiting angular position decreases as the quantum parameter increases but a little bounce occurs after the formation of the wormhole, and the relative magnification in magnitudes first decreases and then increases as the quantum parameter increases.

It is well known that general relativity is an effective theory of gravity at low energy scale, and actually quantum effects cannot be ignored in the strong-field regime. As a strong gravitational object, black hole plays a key role in testing the quantum effects of gravity in the strong-field regime. In this paper, we focus on black hole in effective loop quantum gravity and investigate what the influences are of the quantum effects on the weak and strong bending angles of light rays. We find that this black hole could be a Schwarzschild black hole, a regular black hole, a one-way traversable wormhole, or a two-way traversable wormhole for the different values of the quantum parameter, and the strong bending angle for this compact object exhibits two different divergent behaviors, i.e., the logarithmic divergence and non-logarithmic divergence. There are a series of relativistic images on both sides of the optical axis. Only the outermost one can be resolved as a single image, and all others are packed together at the limiting angular position. It is interesting to note that the angular separation between the outermost relativistic image and the others initially increases and then decreases as the quantum parameter increases, indicating that there is a maximum in the angular separation. The maximum is reached after the black hole becomes a wormhole, which can be taken as a signal for the formation of the wormhole. Moreover, the limiting angular position decreases as the quantum parameter increases but a little bounce occurs after the formation of the wormhole, and the relative magnification in magnitudes first decreases and then increases as the quantum parameter increases.

In this paper, we investigate thick branes generated by a scalar field in mimetic gravity theory, which is inspired by considering the conformal symmetry under the conformal transformation of an auxiliary metric. By introducing two auxiliary super-potentials, we transform the second-order field equations of the system into a set of first-order equations. With this first-order formalism, several types of analytical thick brane solutions are obtained. Then, tensor and scalar perturbations are analyzed. We find that both kinds of perturbations are stable. The effective potentials for the tensor and scalar perturbations are dual to each other. The tensor zero mode can be localized on the brane while the scalar zero mode cannot. Thus, the four-dimensional Newtonian potential can be recovered on the brane.