Spin effects in the phasing formula of eccentric compact binary inspirals up to the third post-Newtonian order

Understand

Compact binary sources that emit gravitational waves (GW) are expected to be both spinning and on eccentric orbits.

• No closed-form expression for the phasing of GWs are available to date that contain information from both spin and eccentricity.
• The introduction of eccentricity can slow waveform generation, often requiring slower numerical methods governing its evolution.
• However, closed-form expressions for the waveform phase can be obtained when eccentricity is treated as a small parameter, enabling quick waveform generation.