On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation

Details On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation

2000-05-10

arxiv.org/abs/gr-qc/0005034v1

Phys.Rev. D62 (2000) 084011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

REVTeX, 25 pages, 3 figures, submitted to Phys. Rev. D

Scientific paper

10.1103/PhysRevD.62.084011

We discuss the analytical determination of the location of the Last Stable Orbit (LSO) in circular general relativistic orbits of two point masses. We use several different ``resummation methods'' (including new ones) based on the consideration of gauge-invariant functions, and compare the results they give at the third post-Newtonian (3PN) approximation of general relativity. Our treatment is based on the 3PN Hamiltonian of Jaranowski and Sch\"afer. One of the new methods we introduce is based on the consideration of the (invariant) function linking the angular momentum and the angular frequency. We also generalize the ``effective one-body'' approach of Buonanno and Damour by introducing a non-minimal (i.e. ``non-geodesic'') effective dynamics at the 3PN level. We find that the location of the LSO sensitively depends on the (currently unknown) value of the dimensionless quantity $\oms$ which parametrizes a certain regularization ambiguity of the 3PN dynamics. We find, however, that all the analytical methods we use numerically agree between themselves if the value of this parameter is $\oms\simeq-9$. This suggests that the correct value of $\oms$ is near -9 (the precise value $\oms^*\equiv-{47/3}+{41/64}\pi^2=-9.3439...$ seems to play a special role). If this is the case, we then show how to further improve the analytical determination of various LSO quantities by using a ``Shanks'' transformation to accelerate the convergence of the successive (already resummed) PN estimates.

Affiliated with

Also associated with

No associations

Rating

On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-636984