| Abstract : | Since the detection of the first gravitational wave event (GW150914), the ground-based network of LIGO-Virgo detectors detected nearly 90 compact binary coalescences (CBCs). A coalescing compact binary can have different phases of evolution that can be suitably divided into three distinct phases: early and late inspiral, merger, and ringdown. While post-Newtonian (PN) theory accurately describes the low-frequency, perturbative early inspiral part, the high-frequency, non-perturbative late-inspiral, and merger-ringdown part is described by Numerical relativity. Different extrinsic and intrinsic parameters, such as eccentricity and spins of binary constituents, potentially modify the gravitational waveform and may lead to significant biases in the analysis of the observed GW data if ignored. Although numerous works have focused on the effect of spins and eccentricity in gravitational waveforms separately within the PN formalism; however, a combined treatment, including spins and eccentricity, is largely absent. In this talk, we present and discuss the computation of all the spin effects, i.e., linear-in-spin (spin-orbit) and quadratic-in-spin (spin-spin), in the spherical harmonic modes of the gravitational waveform valid for general orbits within the PN framework. Also, we extend these general orbit results and specialize to the case of elliptical orbit using generalized quasi-Keplerian representation for the conserved dynamics of the spinning compact binaries in elliptical orbits.
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