Gravitational Waves from Inspiralling Compact Binaries in ... - LUTH

Gauge Invariant Variables
Memmesheimer, Gopakumar and Schäfer (2004) stress use of
gauge invariant variables in the elliptical orbit case
Damour and Schäfer (1988) showed that the functional form of n
and Φ as functions of gauge invariant variables like E and h is the
same in different coordinate systems (gauges).
From the explicit expressions for n and Φ in the ADM and modified
harmonic coordinates the gauge invariance of these two
parameters is explicit at 3PN.
MGS04 suggest the use of variables xMGS = (Gmn/c 3 ) 2/3 and
k ′ = (Φ − 2π)/6π as gauge invariant variables in the general orbit
case.
We propose a variant of the former:
x = (Gmn Φ/2πc 3 ) 2/3 = (Gmn Kc 3 ) 2/3 = (Gmn (1 + k)c 3 ) 2/3 .
Our choice is the obvious generalisation of gauge invariant variable
x in the circular orbit case and thus facilitates the straightforward
reading out of the circular orbit limit.
BRI-IHP06-I – p.43/??