Conventions

An important source of these conventions is Boyle et al. [2], which describes conventions used for SXS waveforms in Appendix C. BMS conventions are described in Mitman et al. [3]. The conventions for the geometric algebra

Nominal values for solar and planetary quantities are given in Prša et al. [4]. Other constants can be found in the lisaconstants package, which otherwise integrates with astropy.

The signature is ${-}{+}{+}{+}$, and we use units where $G=c=1$.

The Christoffel symbols and the Riemann, Ricci, and Weyl tensors follow the Misner-Thorne-Wheeler conventions [5] — Eqs. (14.36), (8.44), (8.47), and (13.50) of that reference, respectively. The Newman-Penrose Weyl components are defined as

\[\begin{aligned} \Psi_0 &= C_{abcd} \ell^a m^b \ell^c m^d, \\ \Psi_1 &= C_{abcd} \ell^a n^b \ell^c m^d, \\ \Psi_2 &= C_{abcd} \ell^a m^b \bar{m}^c n^d, \\ \Psi_3 &= C_{abcd} \ell^a n^b \bar{m}^c n^d, \\ \Psi_4 &= C_{abcd} n^a \bar{m}^b n^c \bar{m}^d. \end{aligned}\]

The metric perturbation is defined as

\[h_{ab} = g_{ab} - \eta_{ab},\]

where $\eta_{ab}$ is the Minkowski metric. The strain components are defined as

\[\begin{aligned} h_+ &= \frac{1}{2} (h_{\hat{\theta}\hat{\theta}} - h_{\hat{\phi}\hat{\phi}}), \\ h_\times &= h_{\hat{\theta}\hat{\phi}}, \\ h &= h_+ - i h_\times. \end{aligned}\]

where the hats indicate orthonormal components in the spherical basis. We have the asymptotic relation

\[\Psi_4 \sim -\ddot{h},\]

where the dots indicate time derivatives.