Particle Trajectories In Curved Spacetime

In the field of astrophysics and cosmology,massive celestial bodies play an im-portant role as gravitational centers.By bending the nearby spacetime,these massive bodies exert their influence on particles traveling around them.Meanwhile,the trajec-tories of particles are also affected by the large-scale structure of our universe.Since there are many particles and massive gravitational centers,it is essential to study the trajectories of particles in curved spacetime.The main contents of this thesis focus on four aspects,they are(1)the gravitational lensing of massive particles,(2)the exit cone in Schwarzschild's spacetime,(3)the circular orbits in static and spherical symmetry spacetime,and(4)the diffuse supernova neutrino background.This thesis is divided into five chapters,including the introduction as the first chapter.In Chapter 2 the gravitational lensing of particles in Schwaxzschild spacetime is studied.It is showed that when particle's speed v changes from subluminal velocity to the speed of light the corresponding trajectories are continuity.Then the existence of a particle sphere as an analog of photon sphere is proved.The fast and slow particle limits and weak and strong lensing limits of the exact formula for the bending angle are studied in a detailed way.The obtained results are applied to the gravitational lensing to show how the velocity correction can affect the deflection angles.At the end of this chapter the potential application of results in determining the mass and mass hierarchy of neutrinos is discussed.In Chapter 3 the particle's exit cone and a classification of trajectories in Schwarzschild spacetime is studied.They both are decided by the radial equation from the geodesic equation system.The radial motion of a particle is showed to be equivalent to the motion of a one-dimensional classical particle in an effective potential.It is found that the radius of the particle and photon sphere is just a maximum of the effective poten-tial.This method of effective potential is then used to obtain the exit angle for both.massive and massless particles,and to demonstrate that the massive/massless particleswill have an exit angel of ?/2 when they are emitted on the particde/photon sphere.Theclassification of trajectories is completed by using the exit angle.In Chapter 4 the existence and stability of circular orbits in static and spherically symmetric spacetime is studied.The start point is the geodesic equations for circularorbits.Some non-existent theorems axe proved.Among them,by adding some restric-tions to the spherical symmetry spacetime,it is concluded that there is always a circularorbit in an asymptotically flat spacetime which has a negative Newtonian potential atinfinity.It is worth to mention that the analysis and results in this chapter are notbased on the explicit form of metric functions,therefore they are vastly applicable tonumerous metrics.In Chapter 5 the feasibility of screening and constraining cosmological models using diffuse supernova neutrino background(DSNB)is discussed.During the propagation ofneutrinos from an exploding supernova to the Earth detector,its trajectory will be affected by the large-scale spacetime structure of the universe.Therefore the metric of the universe have an influence on the DSNB,and then DSNB carries information about the metrics.This relation between DSNB and the metric lays the foundation for using DSNB to screen and constrain the cosmological models.The DSNB flux for different Chaplygin gas models are plotted.the results indicate that there are up to 25%differences around the peaks between different models,which fully demonstrates the experimental feasibility of using DSNB to screening and constraining cosmological models.