Gravitational Waveform and Polarization from Binary Black Hole Inspiral in Dynamical Chern-Simons Gravity: From Generation to Propagation

TL;DR

This paper derives gravitational waveforms and polarization modes from binary black hole inspirals in dynamical Chern-Simons gravity, highlighting modifications during propagation but not generation, with effects appearing at specific post-Newtonian orders.

Contribution

It provides the first detailed calculation of gravitational waveforms and polarization modes in dynamical Chern-Simons gravity, including effects during both generation and propagation.

Findings

No extra polarization modes up to 2PN order.

Parity-violating effects influence waveform during propagation.

Waveform modifications occur at 1.5PN order during propagation.

Abstract

We calculate the gravitational waveform radiated from spinning black holes (BHs) binary in dynamical Chern-Simons (dCS) gravity. The equation of motion (EOM) of the spinining binary BHs is derived based on the modified Mathisson-Papapetrou-Dixon equation for the spin-aligned circular orbits. The leading-order effects induced by the dCS theory contains spin-spin interaction and monopole-quadrupole interaction, which influence both the EOM of the binary system and corresponding gravitational waveform at the second post-Newtonian (PN) order (i.e., 2PN order). After reporting the waveforms, we investigate the polarization modes of gravitational waves (GWs) in dCS theory. None of the extra modes appears in this theory up to the considered PN order. Moreover, since the time scale of the binary merger is much smaller than that of the cosmological expansion, the parity-violating effect of the dCS theory does not appear in the process of GW generation. However, during the process of GW propagation, amplitude birefringence, a typical parity-violating effect, makes plus and cross modes convert to each other, which modifies the gravitational waveform at 1.5PN order.