Modulation of the gravitational waveform by the effect of radiation reaction

When we calculate gravitational waveforms from extreme-mass-ratio inspirals 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 can 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. [Y. Mino, Prog. Theor. Phys. 115, 43 (2006); Y. Mino, Prog. Theor. Phys. 113, 733 (2005); Y. Mino and R. Price (unpublished).] is an appropriate perturbation expansion for studying the radiation reaction effect on the gravitational waveform

POINT ESTIMATION OF THE PROCESS CAPABILITY INDEX C(pk)

In this paper point estimation of the process capability index C(pk) is considered. In order to improve on the natural estimator, a simple alternative estimator is proposed and its mean square error is evaluated numerically

Adiabatic Expansion for Metric Perturbation and the condition to solve the Gauge Problem for Gravitational Radiation Reaction Problem

We examine the adiabatic approximation in the study of a relativistic two-body problem with the gravitational radiation reaction. We recently pointed out that the usual metric perturbation scheme using a perturbation of the stress-energy tensor may not be appropriate for study of the dissipative dynamics of the bodies due to the radiation reaction. We recently proposed a possible approach to solve this problem with a linear black hole perturbation. This paper proposes a non-linear generalization of that method for a general application of this problem. We show that, under a specific gauge condition, the method actually allows us to avoid the gauge problem.Comment: accepted by Progress of Theoretical Physic