2024/08/25 by Noah M. MacKay, MacKay, Noah M.
Physics and Astronomy · #70G75 #83C10 #83C25 #83C35 (Primary) #83C35 (Secondary) #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Pulsars and Gravitational Waves Research
paper · pdf · doi:10.48550/arxiv.2408.13917
openalex publication_date 2024/08/25 · openalex created_date 2024/09/21 · openalex updated_date 2026/07/28
The final pulse of gravitational wave (GW) emission is released at the peak of the chirp rise before compact binary merger. LIGO detections since GW150914 reveal a correlation between the radiated energy Erad and the ad hoc scaling of one-tenth of the chirp mass M, which begs to ask if this is physically grounded. Motivated by current effective one-body models, this work models compact binary coalescence (CBC) as a rotating, compact mass shell that is contracting towards the total mass horizon. Using a variational methodology, the Laplace-Beltrami formulation for the Ricci tensor is applied to a Kerr metric Ansatz, retrieving the energy density T00 of the CB mass shell via the Einstein field equations. At the time of coalescence tC, the corresponding surface energy ultimately depends on the reduced mass μ of the CB, the symmetric mass ratio α, and the CB's normalized orbital spin velocity. In other words, this surface energy is the anticipated energy radiated as GWs, which is not one-tenth of the chirp mass systematically. Under simple assumptions, the anticipated energy for GW150914 -- a representative example -- is 2.08 M_\odot c2 using documented center values. Under a more rigorous analysis in comparison, the anticipated energy for GW150914 is 3.27M_\odot c2. This is compared with the GWTC recorded value of 3.1+0.4-0.4M_\odot c2 for GW150914, with the latter analysis providing a closer approximation to the actual value. This study also includes the derivation of gravitational waveforms from the CB mass shell model, which depend on dynamic frequencies and decreasing CB separations.