摘要
We analytically model a relativistic problem consisting of a point-particle with mass m in close orbit around a stationary Schwarzschild black hole with mass M = 1 using the null-cone formalism when l = 2. We use the -function to model the matter density of the particle. To model the whole problem, we apply the second order differential equation obtained elsewhere for a dynamic thin matter shell around a Schwarzschild black hole. The only thing that changes on the equation is the quasi-normal mode parameter which now represent the orbital frequency of the particle. We compare our results with that of the standard 5.5 PN formalism and found that there is a direct proportionality factor that relates the two results, i.e. the two formalisms.
We analytically model a relativistic problem consisting of a point-particle with mass m in close orbit around a stationary Schwarzschild black hole with mass M = 1 using the null-cone formalism when l = 2. We use the -function to model the matter density of the particle. To model the whole problem, we apply the second order differential equation obtained elsewhere for a dynamic thin matter shell around a Schwarzschild black hole. The only thing that changes on the equation is the quasi-normal mode parameter which now represent the orbital frequency of the particle. We compare our results with that of the standard 5.5 PN formalism and found that there is a direct proportionality factor that relates the two results, i.e. the two formalisms.
