Shadow and Weak Deflection Angle of a Black Hole in Nonlocal Gravity

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.

Extended Gravity Constraints at Different Scales

We review a set of the possible ways to constrain extended gravity models at Galaxy clusters scales (the regime of dark energy explanations and comparison with ΛCDM), for black hole shadows, gravitational wave astronomy, binary pulsars, the Solar system and a Large Hadron Collider (consequences for high-energy physics at TeV scale). The key idea is that modern experimental and observational precise data provide us with the chance to go beyond general relativity.

Constraints on a Tidal Charge of the Supermassive Black Hole in M87* with the EHT Observations in April 2017

More than two years ago the Event Horizon Telescope collaboration presented the first image reconstruction around the shadow for the supermassive black hole in M87*. It gives an opportunity to evaluate the shadow size. Recently, the Event Horizon Telescope collaboration constrained parameters (“charges”) of spherical symmetrical metrics of black holes from an estimated allowed interval for shadow radius from observations of M87* in 2017. Earlier, analytical expressions for the shadow radius as a function of charge (including a tidal one) in the case of Reissner–Nordström metric have been obtained. Some time ago, Bin-Nun proposed to apply a Reissner–Nordström metric with a tidal charge as an alternative to the Schwarzschild metric in Sgr A*. If we assume that a Reissner–Nordström black hole with a tidal charge exists in M87*, therefore, based on results of the shadow size evaluation for M87* done by the Event Horizon Telescope collaboration we constrain a tidal charge. Similarly, we evaluate a tidal charge from shadow size estimates for Sgr A*.

Weak Deflection Angle and Shadow by Tidal Charged Black Hole

In this article, we calculate the deflection angle of a tidal charged black hole (TCBH) in weak field limits. First, we obtain the Gaussian optical curvature and then apply the Gauss–Bonnet theorem on it. With the help of Gibbons–Werner method, we are able to calculate the light’s deflection angle by TCBH in weak field limits. After calculating the deflection angle of light, we check the graphical behavior of TCBH. Moreover, we further find the light’s deflection angle in the presence of the plasma medium and also check the graphical behavior in the presence of the plasma medium. Moreover, we investigate the shadow of TCBH. For calculating the shadow, we first find the null geodesics around the TCBH and then find its shadow radius. We also obtain TCBH’s shadow in the plasma medium. Hence, we discuss the shadow of the TCBH, using the M87* parameters announced by the event horizon telescope.

Black Holes and Wormholes in Extended Gravity

We discuss black hole type solutions and wormhole type ones in the effective gravity models. Such models appear during the attempts to construct the quantum theory of gravity. The mentioned solutions, being, mostly, the perturbative generalisations of well-known ones in general relativity, carry out additional set of parameters and, therefore could help, for example, in the studying of the last stages of Hawking evaporation, in extracting the possibilities for the experimental or observational search and in helping to constrain by astrophysical data.

Constraints on tidal charge of the supermassive black hole at the Galactic Center with trajectories of bright stars

As it was pointed out recently in Hees et al. (Phys Rev Lett 118:211101, 2017), observations of stars near the Galactic Center with current and future facilities provide an unique tool to test general relativity (GR) and alternative theories of gravity in a strong gravitational field regime. In particular, the authors showed that the Yukawa gravity could be constrained with Keck and TMT observations. Some time ago, Dadhich et al. (Phys Lett B 487:1, 2001) showed that the Reissner-Nordström metric with a tidal charge is naturally appeared in the framework of Randall-Sundrum model with an extra dimension ( Q 2 is called tidal charge and it could be negative in such an approach). Astrophysical consequences of presence of black holes with a tidal charge are considerered, in particular, geodesics and shadows in Kerr-Newman braneworld metric are analyzed in Schee and Stuchlík (Intern J Mod Phys D 18:983, 2009), while profiles of emission lines generated by rings orbiting braneworld Kerr black hole are considered in Schee and Stuchlík (Gen Relat Grav 52:1795, 2009). Possible observational signatures of gravitational lensing in a presence of the Reissner-Nordström black hole with a tidal charge at the Galactic Center are discussed in papers (Bin-Nun in Phys Rev D 81:123011, 2010; Bin-Nun in Phys Rev D 82:064009, 2010; Bin-Nun in Class Quant Grav 28:114003, 2011). Here we are following such an approach and we obtain analytical expressions for orbital precession for Reissner-Nordström-de-Sitter solution in post-Newtonian approximation and discuss opportunities to constrain parameters of the metric from observations of bright stars with current and future astrometric observational facilities such as VLT, Keck, GRAVITY, E-ELT and TMT.