Orateur
Description
Compact binaries are the primary sources of gravitational waves measured by gravitational-wave detectors. In this context, obtaining the equations of motion in different approximation schemes is essential for producing waveform templates with the accuracy required by future detections, constituting a precision test of general relativity.
In this presentation, I derive the gravitational radiation-reaction force on a compact binary system at 4.5PN order, i.e., 2PN orders beyond the leading 2.5PN radiation-reaction term in harmonic coordinates. This result is derived using the 4.5PN gravitational radiation-reaction force in the Burke–Thorne (BT) coordinate system.
This represents a significant improvement, as harmonic coordinates provide a manifestly Lorentz-invariant formulation and offer a much simpler expression compared to the BT coordinates. Moreover, they pave the way for comparisons with other approximation schemes (such as post-Minkowskian or gravitational self-force) at 4.5PN.
Using the harmonic radiation-reaction acceleration, we also derive from first principles the flux-balance laws and the center-of-mass position, in a general frame and up to the 4.5PN order.