Repulsive Effect For Particles In The Kerr-Taub-NUT Spacetime And Gravitational Lensing By A Black Hole With Torsion

Black hole physics is one of the most active research areas in astrophysics.It is located in the intersection of many fields such as general relativity,quantum mechanics,string theory,and statistical physics,and it occupies an important position in modern physics.Black hole jet is a very spectacular astronomical phenomenon.The reason of the formation of the black hole jet is very complex and can be understood as a comprehensive effect produced by a variety of physical processes.The non-magnetic-based repulsive effects of particles near the axis of the rotating black hole may play an important role in the formation of black hole jets.The gravitational lensing effect is a phenomenon in which light ray deflects as it passes through a gravitational field.It can help us to observe distant and gloomy objects.It can also be applied to detect the distribution of dark matter in the universe,determine the cosmological constants,and identify various gravitational theories.In this Paper we have investigated the repulsive effect for particles in the Kerr-Taub-NUT(KTN)spacetime and the gravitational lensing effect by a black hole with torsion under the generalized Einstein-Cartan-Kibble-Sciama(ECKS)theory of gravity respectively.In Chapter 1,we briefly introduce the black hole jet and the gravitational lensing and their basic research methods.In Chapter 2,we study the repulsive effect of particles in the KTN black hole.We find that for particles located at the intersection of the outer surface of the KTN black hole ergosphere and the rotation axis and the intersection of the outer surface of the ergosphere and the equatorial plane,the acceleration of the particles and the influence of the NUT charge n on the acceleration of the particles depends on the value of the Carter constant.For particles located at the equatorial plane,whether the presence of the NUT charge n increases their acceleration depends on the axial velocity of the particles.We also present numerically the changes of the observable velocity,the proper acceleration and the observable acceleration with the NUT charge for the unbound particles in the Kerr-Taub-NUT spacetime.With the increase of the NUT charge n,the observable velocity ?z(z)increases monotonously.For the proper acceleration z(z),we find that it decreases with n for the smaller z,while it increases for larger z.The observable acceleration ?z'increases with n in the regions with the small z and the large z but it decreases in the intermediate region of z.In Chapter 3,under the generalized ECKS theory of gravity,we investigate the gravitational lensing by two static spherically symmetric spacetimes with tortion.We find that the torsion parameters change the spacetime structure and the photon trajectories.For the two spacetimes,the existence conditions of the horizon and the photon sphere are inconsistent,so there are four regions in the parameter space.They are(1)a black hole spacetime with event horizon and photon sphere,(2)a black hole with event horizon but no photon sphere,(3)a naked singularity with photon sphere but no event horizon(weak naked singularity)and(4)a naked singularity without event horizon and photon sphere(strong naked singularity)respectively.Among which,The black hole spacetime with event horizon but no photon sphere has not yet appeared in the existing literature.When photon sphere exisits,the deflection angle of the light ray diverges logarithmically near the photon sphere for both of the spacetimes.In the strong naked singularity case,the deflection angle of the light ray closing to the singularity in both of the spacetimes with torsion we studied tends to a fixed value-?,which is consistent with the case of the static strong naked singularity in the existing literature.When the spacetime is a black hole with event horizon but no photon sphere,the deflection angle of the light ray near the event horizon diverges logarithmically in the spacetime discovered by H.Shabani et al,but the coefficients in the strong-field limit are different from those in the case with photon sphere.In addition,negative deflection angles occur when the torsion parameters takes certain specific values,which is different from the situation in the usual spacetimes.While in the other spacetime with torsion,the deflection angle of the light ray near the event horizon does not diverge,but tends to a finite value.Finally,we summarize the two studies of the repulsive effect for particles in the Kerr-Taub-NUT spacetime and the gravitational lensing by a black hole with torsion and look forward to future researches.