Black Hole Shadow And Energy Extraction

The detection of gravitational waves and the image of black hole confirm the existence of black holes in the universe.The study of black hole and its related physics can not only explore the physical phenomena in the strong gravitational field,but also verify the gravitational theory such as general relativity.In this paper,we first studied the shadow of a rotating squashed Kaluza-Klein black hole and a disformal Kerr black hole in quadratic degenerate higher-order scalar-tensor theories.Then we studied the electromagnetic line emissions from near-horizon region in the extremal Kerr-Taub-NUT black hole spacetime and the energy extraction from a Konoplya-Zhidenko rotating non-Kerr black hole.The main results are listed as follows:Firstly,in the study of the shadow of a rotating squashed Kaluza-Klein black hole,we find that:(i)The black hole shadow is a perfect disk shape under different rotation parameters,which is a new feature different from the four-dimensional rotating black hole in general relativity where the shape of the shadow is non-circular.(ii)The shadow of a rotating squashed KK black hole is heavily influenced by the extra dimension.Especially,as the black hole parameters lie in a certain special range,we find that there is no shadow for a black hole since the minimum value of shadow radius is zero,which is novel since it does not emerge in the usual black hole spacetimes.(iii)In the cases with zero or the larger rotation parameter,we find that the shadow radius varies monotonically with the rotation parameter.In the cases with the smaller rotation parameter,the shadow radius first decreases and then increases with the rotation parameter.Finally,combining with the supermassive black hole in M87 and Sgr A*,we estimate the angular radius of the shadow of these supermassive black holes with different extra dimension parameters.Secondly,in studied the shadow of a disformal Kerr black hole,which belongs to non-stealth rotating solutions in quadratic degenerate higher-order scalar-tensor(DHOST)theory.We find that:(i)the size of the shadow increases with the de-formation parameter for the black hole with fixed spin parameter.(ii)The larger the black hole rotation parameter is,the more obvious the shadow shape changes with the deformation parameter;The distortion parameters?_sfirst increases and then decreases with the deformation parameter.Especially,when the fast rotating black hole with negative deformation parameter,we find that there exist a“pedicel”-like structure appeared in the shadow.(iii)When the parameters of black hole and defor-mation parameter take some special values,we find that there exist the self-similar fractal structures in the shadow.These features in the black hole shadow originating from the scalar field could help us to understand the shadow of the disformal Kerr black hole and the quadratic DHOST theory.Thirdly,we studied electromagnetic line emissions from near-horizon region in the extremal Kerr-Taub-NUT black hole spacetime.We find that:(i)For the fixed NUT charge,one can find that the flux increases with the angular coordinate?₀of the observer's position,which implies that electromagnetic line emission for the observer in the Southern Hemisphere is brighter than that in the Northern one.This is a new observation feature of electromagnetic line emissions at the NHEKTNline of KTN black hole,which is different from that in the Kerr case where the electromagnetic line emission is the same for the symmetrical observers on both sides of the equatorial plane.This is due to the fact that the KTN space-time metric is no longer symmetrical about the equatorial plane.(ii)For fixed the intermediate redshift factor g,as the observer lies in the Southern Hemisphere,the flux F_odecreases monotonously with n;as the observer lies in the Northern Hemisphere,the flux F_ofirst increases and then decreases with n.Fourthly,we studied the Penrose process and the energy extraction from a Konoplya-Zhidenko rotating non-Kerr black hole.We find that:(i)With the in-crease of the deformation parameter,the maximum efficiency of energy extraction in Penrose process decreases,which differs from that in the Johannsen-Psaltis rotating non-Kerr spacetime where the maximum efficiency increases with the deformation parameter.Therefore,the deformation parameters of different black hole spacetime have different effects on the energy extraction efficiency.(ii)In the case of super-spinning and the positive deformation parameter is close to zero,we find that the maximum efficiency(?)_max?(?).Since the radius of the event horizon is very small at this time,the maximum efficiency of energy extraction is almost infinite,which is much higher than 20.7%in Kerr spacetime.Finally,we presented a summary and make some prospects for the investigation.