The Gravitational Radiation Emitted by a System Consisting of a Point Particle in Close Orbit around a Schwarzschild Black Hole

Amos S. Kubeka

Department of Mathematical Sciences, University of South Africa, Pretoria, South Africa.

DOI: 10.4236/jmp.2012.310186                

Abstract

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.

Keywords

Null Formalism; Gravitational Radiation; Schwarzschild Black Hole; PN Formalism; Delta Function; Point Particle; Bondi Mass

Conflicts of Interest

The authors declare no conflicts of interest.

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