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SpECTRE
v2025.03.17
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Compute the Weyl scalar \(\Psi_1\) in the volume according to the standard set of Newman-Penrose vectors. More...
#include <NewmanPenrose.hpp>
Public Types | |
| using | return_tags = tmpl::list< Tags::Psi1 > |
| using | argument_tags = tmpl::list< Tags::BondiJ, Tags::Dy< Tags::BondiJ >, Tags::BondiK, Tags::BondiQ, Tags::Dy< Tags::BondiQ >, Tags::BondiR, Tags::EthRDividedByR, Tags::Dy< Tags::BondiBeta >, Spectral::Swsh::Tags::Derivative< Tags::BondiBeta, Spectral::Swsh::Tags::Eth >, Spectral::Swsh::Tags::Derivative< Tags::Dy< Tags::BondiBeta >, Spectral::Swsh::Tags::Eth >, Tags::OneMinusY > |
Static Public Member Functions | |
| static void | apply (gsl::not_null< Scalar< SpinWeighted< ComplexDataVector, 1 > > * > psi_1, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &bondi_j, const Scalar< SpinWeighted< ComplexDataVector, 2 > > &dy_j, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &bondi_k, const Scalar< SpinWeighted< ComplexDataVector, 1 > > &bondi_q, const Scalar< SpinWeighted< ComplexDataVector, 1 > > &dy_q, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &bondi_r, const Scalar< SpinWeighted< ComplexDataVector, 1 > > ð_r_divided_by_r, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &dy_beta, const Scalar< SpinWeighted< ComplexDataVector, 1 > > ð_beta, const Scalar< SpinWeighted< ComplexDataVector, 1 > > ð_dy_beta, const Scalar< SpinWeighted< ComplexDataVector, 0 > > &one_minus_y) |
Compute the Weyl scalar \(\Psi_1\) in the volume according to the standard set of Newman-Penrose vectors.
Our convention is \(\Psi_1 = l^\alpha n^\beta l^\mu m^\nu C_{\alpha \beta \mu \nu}\).
\begin{align*} \Psi_1 = &\frac{(1-y)^2}{\sqrt{128} \sqrt{1 + K} R^2}\Bigg\{ J(\bar{\eth }\beta + \tfrac{1}{2} \bar{Q}) - (1 + K) (\eth \beta + \tfrac{1}{2} Q) \\ &+(1-y)\Bigg[ (1 + K)\eth\partial_{y}\beta - J\bar{\eth }\partial_{y}\beta + \left(- J \frac{\bar{\eth} R}{R} + (1 + K) \frac{\eth R}{R}\right) \partial_{y}\beta \\ &\quad + \frac{1}{4K}\Bigg( J\left\{ -2 \partial_{y}\bar{Q} + \partial_{y}\bar{J} [2 (\eth\beta + \tfrac{1}{2}Q) + J(\bar{\eth}\beta + \tfrac{1}{2} \bar{Q})] \right\}\\ &\qquad +(1+K)\Big\{ 2 (\partial_{y}Q + J \partial_{y}\bar{Q}) + (\bar{J} \partial_{y}J - J \partial_{y}\bar{J}) (\eth\beta + \tfrac{1}{2} Q) \\ &\qquad\quad - (1+K) [2 \partial_{y}Q + \partial _{y}J (\bar{\eth }\beta + \tfrac{1}{2} \bar{Q})] \Big\}\Bigg)\Bigg]\Bigg\} \end{align*}