Modulation of the gravitational waveform by the effect of radiation reaction
Abstract
When we calculate the gravitational waveform from the extreme-mass-ratio inspirals (EMRIs) by metric perturbation, it is a common strategy to use the adiabatic approximation. By the adiabatic approximation, we first calculate the waveform by the linear metric perturbation induced by geodesics orbiting a black hole, then we calculate the adiabatic evolution of the parameters of geodesics due to the radiation reaction effect through the calculation of the self-force. This procedure is considered to be reasonable, however, there is no direct proof that it can actually produce the correct waveform we would observe. In this paper, we study the formal expression of the second order metric perturbation and show that the waveform by the second order metric perturbation does have the feature that the linear metric perturbation is actually modulated by the adiabatic evolution of the geodesic. This evidence supports that the adiabatic approximation can actually produce the correct waveform and that the adiabatic expansion we propose is a more appropriate perturbation expansion to study the radiation reaction effect on the gravitational waveform.Keywords
All Related Versions
This publication has 0 references indexed in Scilit: