Abstract
The metric perturbation induced by a particle in the Schwarzschild background is usually calculated in the Regge-Wheeler (RW) gauge, whereas the gravitational self-force is known to be given by the tail part of the metric perturbation in the harmonic gauge. Thus, to identify the gravitational self-force correctly in a specified gauge, it is necessary to find out a gauge transformation that connects these two gauges. This is called the gauge problem. As a direct approach to solve the gauge problem, we formulate a method to calculate the metric perturbation in the harmonic gauge on the Schwarzschild background. We apply the Fourier-harmonic expansion to the metric perturbation and reduce the problem to the gauge transformation of the Fourier-harmonic coefficients (radial functions) from the RW gauge to the harmonic gauge. We derive a set of decoupled radial equations for the gauge transformation. These equations are found to have a simple second-order form for the odd parity part and the forms of spin s = 0 and 1 Teukolsky equations for the even parity part. As a by-product, we correct typographical errors in Zerilli's paper and present a set of corrected equations in Appendix A.
| Original language | English |
|---|---|
| Article number | 104017 |
| Journal | Physical Review D |
| Volume | 68 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - Dec 1 2003 |
| Externally published | Yes |
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All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)
Cite this
Gauge problem in the gravitational self-force : Harmonic gauge approach in the Schwarzschild background. / Sago, Norichika; Nakano, Hiroyuki; Sasaki, Misao.
In: Physical Review D, Vol. 68, No. 10, 104017, 01.12.2003.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Gauge problem in the gravitational self-force
T2 - Harmonic gauge approach in the Schwarzschild background
AU - Sago, Norichika
AU - Nakano, Hiroyuki
AU - Sasaki, Misao
PY - 2003/12/1
Y1 - 2003/12/1
N2 - The metric perturbation induced by a particle in the Schwarzschild background is usually calculated in the Regge-Wheeler (RW) gauge, whereas the gravitational self-force is known to be given by the tail part of the metric perturbation in the harmonic gauge. Thus, to identify the gravitational self-force correctly in a specified gauge, it is necessary to find out a gauge transformation that connects these two gauges. This is called the gauge problem. As a direct approach to solve the gauge problem, we formulate a method to calculate the metric perturbation in the harmonic gauge on the Schwarzschild background. We apply the Fourier-harmonic expansion to the metric perturbation and reduce the problem to the gauge transformation of the Fourier-harmonic coefficients (radial functions) from the RW gauge to the harmonic gauge. We derive a set of decoupled radial equations for the gauge transformation. These equations are found to have a simple second-order form for the odd parity part and the forms of spin s = 0 and 1 Teukolsky equations for the even parity part. As a by-product, we correct typographical errors in Zerilli's paper and present a set of corrected equations in Appendix A.
AB - The metric perturbation induced by a particle in the Schwarzschild background is usually calculated in the Regge-Wheeler (RW) gauge, whereas the gravitational self-force is known to be given by the tail part of the metric perturbation in the harmonic gauge. Thus, to identify the gravitational self-force correctly in a specified gauge, it is necessary to find out a gauge transformation that connects these two gauges. This is called the gauge problem. As a direct approach to solve the gauge problem, we formulate a method to calculate the metric perturbation in the harmonic gauge on the Schwarzschild background. We apply the Fourier-harmonic expansion to the metric perturbation and reduce the problem to the gauge transformation of the Fourier-harmonic coefficients (radial functions) from the RW gauge to the harmonic gauge. We derive a set of decoupled radial equations for the gauge transformation. These equations are found to have a simple second-order form for the odd parity part and the forms of spin s = 0 and 1 Teukolsky equations for the even parity part. As a by-product, we correct typographical errors in Zerilli's paper and present a set of corrected equations in Appendix A.
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U2 - 10.1103/PhysRevD.68.104017
DO - 10.1103/PhysRevD.68.104017
M3 - Article
AN - SCOPUS:33750388091
VL - 68
JO - Physical Review D - Particles, Fields, Gravitation and Cosmology
JF - Physical Review D - Particles, Fields, Gravitation and Cosmology
SN - 1550-7998
IS - 10
M1 - 104017
ER -