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

Method of variation of constants
To do the phasing, solve the evolution equations for {c1, c2, cl, cλ}, on the 2PN
accurate orbital dynamics. This leads to an evolution system, in which the
RHS contains terms of order
O(c −5 ) × 1 + O(c −2 ) + O(c −4 ) = O(c −5 ) + O(c −7 ) + O(c −9 ).
As a first step, restrict attention to the leading order contributions to ¯ Gα and
˜Gα, which define the evolution of {¯cα, ˜cα} under GRR to O(c −5 ) order.
Impose these variations, on to h× and h+. This will allow to obtain GW
polarizations, which are Newtonian accurate in their amplitudes and 2.5PN
accurate in orbital dynamics. 2.5PN accurate phasing of GW. Since ˜ Gα’s
create only periodic 2.5PN corrections to the dynamics, Later look at the
consequences of considering PN corrections to ¯ Gα by computing O(c −9 )
contributions to relevant d¯cα
dt . This is required as ¯ Gα directly contribute to the
highly important adiabatic evolution of h× and h+.
Two constants c1 and c2 assumed to be energy and the angular momentum.
Any functions of these conserved quantities can do as well. Convenient to
use as c1 the mean motion n, and as c2 the time-eccentricity et. Will require
to express 2PN accurate orbital dynamics in terms of l, n and et. Evolution
equations for dn det , dt dt , dcl dt and dcλ in terms of l, n and et.
dt
BRI-IHP06-I – p.114/??