Explicit Field Realizations Of W Strings And The Strong Gravitational Effects In The Black Hole Background

In this thesis, we focus on the realizations of W strings with the scalar fields and spinor fields, and the constructions of their Becchi-Rouet-Stora-Tyutin (BRST) charges, as well as the strong gravitational effects in the black hole background.In the first part of this thesis, the realizations of W2.s strings are studied. Firstly, we investigate the scalar field realizations and spinor field realizations of Virasoro and W2:s algebras, respectively. The results show that the BRST method is not only effective for the scalar field realizations, but also for spinor field realizations. Secondly, by means of the nilpotent nature and the grading form of BRST charge QB=Q0+Q1, we first obtain the spinor realizations of W2,s strings and their BRST charges. Thirdly, based on the linear W1.2,s algebra, we realize the W2.s strings with double scalar fields and spinor fields, respectively. In addition, after re-scaling the spin-s currents, we also study WM2,s (?) WL2,s string systems. The realizations of the Licuville subsystems are obtained at the singularities of the central charge. The physical states of the subsystems are also discussed. This is the new international development of W strings.The second part is devoted to the study of strong gravitational effects of the current international gravity academic attention, the black hole accelerators and strong gravita-tional lensing. The researches include:Firstly, the center-of-mass energy of collision for two particles falling freely from rest at infinity in the black hole background is considered. Our study indicates that for Kerr-Newman (KN) black hole, in order to get an unlimited center-of-mass energy, one of the colliding particles needs to have a critical angular momentum, and the extreme black hole spin parameter also needs to satisfy a constraint. But, after taking into account the back-reaction effect, the center-of-mass energy will be greatly reduced to below the Planck- scale, which will destroy the KN black hole as a high energy scale particle accelerator. While, for the stringy black hole, taking into account the back-reaction effects, a nearly extreme black hole can be used as a very high energy particle accelerator. The results provide a probe Planck energy scale physical mechanism, and provide an effective way to use astronomical observations to study the physics of high energy scale.Secondly, using the equations of motion of photons in curved spacetime, we study the strong gravitational lensing for the static, spherically symmetric spacetime and sta-tionary axisymmetric spacetime, respectively. A direct relationship is established between the high-energy absorption cross section and the static, spherically symmetric black hole lensing. Through this relationship, we can transform the theoretical research of the high-energy absorption cross section into the astronomical observations of the black hole lens-ing. Furthermore, we also study the strong gravitational lensing by the Kerr black hole pierced by a cosmic string. The deflection angle and the astronomical observables are calculated. By means of reverse trajectory of the photon, we examine the critical curves and caustics for the lensing. These results provide a theoretical basis for the astronomical observations.