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SpECTRE
v2025.08.19
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Compute the Weyl scalar \(\Psi_2\) in the volume according to the standard set of Newman-Penrose vectors. More...
#include <NewmanPenrose.hpp>
Public Types | |
| using | return_tags = tmpl::list< Tags::Psi2 > |
| using | argument_tags = tmpl::list< Tags::BondiJ, Tags::BondiK, Tags::BondiR, Tags::Dy< Tags::NewmanPenroseMu >, Spectral::Swsh::Tags::Derivative< Tags::NewmanPenrosePi, Spectral::Swsh::Tags::Eth >, Spectral::Swsh::Tags::Derivative< Tags::NewmanPenrosePi, Spectral::Swsh::Tags::Ethbar >, Tags::NewmanPenroseAlpha, Tags::NewmanPenroseBeta, Tags::NewmanPenroseEpsilon, Tags::NewmanPenroseSigma, Tags::NewmanPenroseRho, Tags::NewmanPenrosePi, Tags::NewmanPenroseMu, Tags::NewmanPenroseLambda, Tags::OneMinusY > |
Compute the Weyl scalar \(\Psi_2\) in the volume according to the standard set of Newman-Penrose vectors.
Our convention is \(\Psi_2 = l^\alpha m^\beta \bar{m}^\mu n^\nu C_{\alpha \beta \mu \nu}\).
\begin{align} \Psi_2 = {}&\frac{1-y}{4 R} \left[ \sqrt{2}(1-y)\partial_y \mu + \sqrt{1+K}\eth\pi - \frac{J}{\sqrt{1+K}}\bar{\eth}\pi\right] \nonumber \\ & {}+ (\epsilon^{SW}+\bar{\epsilon}^{SW}-\bar{\rho})\mu + (\bar{\alpha}^{SW}-\beta^{SW}_{NP}-\bar{\pi})\pi - \sigma\lambda + \nu\kappa \end{align}
In our choice of tetrad, \(\kappa=0\), so the final term is omitted.