Modulation of the gravitational waveform by the effect of radiation reaction

Abstract

When we calculate gravitational waveforms from extreme-mass-ratio inspirals (EMRIs) by metric perturbation, it is a common strategy to use the adiabatic approximation. Under that approximation, we first calculate 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 it be expressed as the linear metric perturbation modulated by the adiabatic evolution of the geodesic. This evidence supports the assumption that the adiabatic approximation can produce the correct waveform, and that the adiabatic expansion we propose in Ref.\cite{adi} is an appropriate perturbation expansion for studying the radiation reaction effect on the gravitational waveform.

Expressions are corrected for easier reading

References in corpus (3)

• Scalar self-force on eccentric geodesics in Schwarzschild spacetime: a time-domain computation
• Second-order gravitational self-force
• Construction of the second-order gravitational perturbations produced by a compact object

Cited by in corpus (6)

• Intermediate-mass-ratio black hole binaries: intertwining numerical and perturbative techniques
• Adiabatic waveforms from extreme-mass-ratio inspirals: an analytical approach
• Two-timescale adiabatic expansion of a scalar field model
• Regular second order perturbations of binary black holes: The extreme mass ratio regime
• Verifying black hole orbits with gravitational spectroscopy
• Gravitational waveforms from periodic orbits around a novel regular black hole