3 research outputs found
Complete adiabatic waveform templates for a test-mass in the Schwarzschild spacetime: VIRGO and Advanced LIGO studies
Post-Newtonian expansions of the binding energy and gravitational wave flux
truncated at the {\it same relative} post-Newtonian order form the basis of the
{\it standard adiabatic} approximation to the phasing of gravitational waves
from inspiralling compact binaries. Viewed in terms of the dynamics of the
binary, the standard approximation is equivalent to neglecting certain
conservative post-Newtonian terms in the acceleration. In an earlier work, we
had proposed a new {\it complete adiabatic} approximant constructed from the
energy and flux functions. At the leading order it employs the 2PN energy
function rather than the 0PN one in the standard approximation, so that,
effectively the approximation corresponds to the dynamics where there are no
missing post-Newtonian terms in the acceleration. In this paper, we compare the
overlaps of the standard and complete adiabatic templates with the exact
waveform in the adiabatic approximation of a test-mass motion in the
Schwarzschild spacetime, for the VIRGO and the Advanced LIGO noise spectra. It
is found that the complete adiabatic approximants lead to a remarkable
improvement in the {\it effectualness} at lower PN ( 3PN) orders, while
standard approximants of order 3PN provide a good lower-bound to the
complete approximants for the construction of effectual templates. {\it
Faithfulness} of complete approximants is better than that of standard
approximants except for a few post-Newtonian orders. Standard and complete
approximants beyond the adiabatic approximation are also studied using the
Lagrangian templates of Buonanno, Chen and Vallisneri.Comment: Proceedings of the GWDAW-9, Accepted for publication in Class. Quant.
Gra
Spacetime Symmetries and Kepler's Third Law
The curved spacetime geometry of a system of two point masses moving on a
circular orbit has a helical symmetry. We show how Kepler's third law for
circular motion, and its generalization in post-Newtonian theory, can be
recovered from a simple, covariant condition on the norm of the associated
helical Killing vector field. This unusual derivation can be used to illustrate
some concepts of prime importance in a general relativity course, including
those of Killing field, covariance, coordinate dependence, and gravitational
redshift.Comment: 11 pages, 3 figures; minor changes and text improvements; matches
version to appear in Class. Quant. Gra