Journal of Modern Physics, 2013, 4, 1119-1122

http://dx.doi.org/10.4236/jmp.2013.48150 Published Online August 2013 (http://www.scirp.org/journal/jmp)

Erratum: 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

Email: kubekas@unisa.ac.za

Received January 8, 2013; revised March 4, 2013; accepted May 26, 2013

Copyright © 2013 Amos S. Kubeka. This is an open access article distributed under the Creative Commons Attribution License,

which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

ABSTRACT

We correct from the previous paper: the first, second and third order derivatives of the Bondi metric function J at the

ISCO of the binary system consisting of a Schwarzschild black hole and a point particle. Previously, these derivatives

where not correctly determined and that resulted in the incorrect determination of the emitted gravitational radiation at

null infinity. The now correctly calculated gravitational radiation is now in full agreement with that obtained by the

standard 5.5 PN formalism to about ninety eight percent. The small percentage difference observed is due to the slow

convergence property of the PN formalism as compared to the null cone formalism, otherwise the results are basically

the same.

Keywords: Black Hole; Particle; Gravitational Radiation; Null Infinity

1. Errors

1) Equation (13) in [1] should be correctly read as

2

d2

=127 8

d12

vv i

vxx

xx

xx

v

(1)

where

is the orbital frequency of the system.

2) Also in the original paper by the author [1], there

was an inherent numerical error due to the incorrect

determination of the first, second, and third order

derivatives of the Bondi metric function

0

x

and

0

x

in

0

0

41 2

96 7.

xccxcJx

xccxcJx

(2)

The correct derivatives are now here given by

0

d,

d

vs

Jx

xsvs

2

2

0

d

dd,

d

vs svs

s

Jx

xsvssvs

(3)

2

2

3

02

2

dd dd

dd

ddd

2

d

,

vs vsvs vs

vs

ss

svs ss

Jx

xsvssv s

svs svs

sv ssv s

svssvs

(4)

and

C

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