Particle Collisions And Accelerating,Strong Gravitational Lensing Effect In Cured Space-time And Energy Extraction From Black Holes

Black hole physics, as an intersectional field of general rela-tivity, quantum mechanics, particle physics, thermodynamics and statistics, is the frontier and hot research field of physics. Focus-ing on black hole physics can help us to understand the nature and laws of some basic issues of the physics, and can also make these disciplines gain a more comprehensive and coordinated de-velopment. This thesis is devoted to investigate three problems concerned by physicists, namely, particle collisions and acceler-ating, the strong gravitational lensing in the curved spacetime and energy extraction from black holes. The results are listed as follows:Firstly, we introduce the hypothesis proposed by Banados, Silk and West (BSW) about the particle accelerators on the back-ground of black hole. Based on BSW mechanism, we study the collision of two particles with the different rest masses moving in the equatorial plane of a Kerr-Taub-NUT spacetime and get the center-of-mass (CM) energy for the particles. We find that the CM energy depends not only on the rotation parameter of the black hole, a, but also on the NUT charge of the Kerr-Taub-NUT spacetime, n. Especially, for the extremal Kerr-Taub-NUT space-time, an unlimited CM energy can be approached if the parameter a is in the range [1,(?)2] and the parameter n is in the range [0,1], which is different from that of the Kerr and Kerr-Newman black holes. At the same time, we study the collision of two general geodesic particles around the Kerr-Newman black hole and get the CM energy of the non-marginally and marginally bound crit-ical particles in the direct collision and LSO collision scenarios. We also find the constraint conditions that arbitrarily high CM energy can be obtained for the near-horizon collision of two gen-eral geodesic particles in the extremal Kerr-Newman black hole. Note that the charge decreases the value of the latitude in which arbitrarily high CM energy can occur, and collision area is located in the north and south of the equator symmetrical latitudes.Secondly, we investigate the strong gravitational lensing on the background of the quasi-Kerr compacted objects. Assuming that the massive compact object at the center of our galaxy can be described by quasi-Kerr spacetime, we obtain the photon radius, the coefficients and observable quantities of the strong gravita-tional lensing. At the same time, we estimate the astronomical observation of the relativistic image and analyse the feasibility of observation. Moreover, as the quadrupolar correction parame-ter ξ becomes negative the radius of the photon sphere becomes smaller, which implies that the photons are more easily captured by the quasi-Kerr compact object with the negative quadrupo-lar correction parameter ξ than that of the Kerr black hole. It is interesting to note that, when the quadrupolar correction pa-rameter ξ takes the positive (negative) value, the photon-sphere radius rps, the minimum impact parameter ups, the coefficient b, the relative magnitudes rm and the angular position of the rela-tivistic images θ∞are larger (smaller) than the results obtained in the Kerr black hole, but the coefficient a, the deflection an-gle α(θ) and the angular separation s are smaller (larger) than that of the Kerr black hole. Based on the above results, we come to the conclusion that there are some significant effects of the quadrupolar correction parameter ξ on the coefficients and ob-servable parameters of the strong gravitational lensing. These results, in principle, may provide a possibility to test how astro-nomical black holes with arbitrary quadrupole moments deviate from the Kerr black hole in the future astronomical observations.Finally, based on Penrose process, the properties of the er-gosphere and the energy extraction by Penrose process in a ro-tating non-Kerr black hole are investigated. It is shown that the ergosphere is sensitive to the deformation parameter and the relative shape of the ergosphere becomes thick with increase of the parameter∈. It is of interest to note that, comparing with the Kerr black hole, the deformation parameter∈enhances the maximum efficiency of the energy extraction process greatly. Es-pecially, for the case of a> M, the non-Kerr metric describes a superspining compact object and the maximum efficiency can exceed60%, while it is only20.7%for the extremal Kerr black hole. This results may provide a possibility to test whether an astronomical black hole is described by Kerr black holes in the general relativity.