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SpECTRE
v2024.05.11
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Superposition of multiple punctures. More...
#include <MultiplePunctures.hpp>
Classes | |
| struct | Punctures |
Public Types | |
| using | options = tmpl::list< Punctures > |
Public Member Functions | |
| MultiplePunctures (const MultiplePunctures &)=default | |
| MultiplePunctures & | operator= (const MultiplePunctures &)=default |
| MultiplePunctures (MultiplePunctures &&)=default | |
| MultiplePunctures & | operator= (MultiplePunctures &&)=default |
| MultiplePunctures (std::vector< Puncture > punctures) | |
| MultiplePunctures (CkMigrateMessage *m) | |
| WRAPPED_PUPable_decl_template (MultiplePunctures) | |
| template<typename... RequestedTags> | |
| tuples::TaggedTuple< RequestedTags... > | variables (const tnsr::I< DataVector, 3, Frame::Inertial > &x, tmpl::list< RequestedTags... >) const |
| template<typename... RequestedTags> | |
| tuples::TaggedTuple< RequestedTags... > | variables (const tnsr::I< DataVector, 3, Frame::Inertial > &x, const Mesh< 3 > &, const InverseJacobian< DataVector, 3, Frame::ElementLogical, Frame::Inertial > &, tmpl::list< RequestedTags... >) const |
| void | pup (PUP::er &p) override |
| const std::vector< Puncture > & | punctures () const |
Static Public Attributes | |
| static constexpr Options::String | help = "Any number of black holes" |
Superposition of multiple punctures.
This class provides the source fields \(\alpha\) and \(\beta\) for the puncture equation (see Punctures) representing any number of black holes. Each black hole is characterized by its "puncture mass" (or "bare mass") \(M_I\), position \(\mathbf{C}_I\), linear momentum \(\mathbf{P}_I\), and angular momentum \(\mathbf{S}_I\). The corresponding Bowen-York solution to the momentum constraint for the conformal traceless extrinsic curvature is:
\begin{equation} \bar{A}^{ij} = \frac{3}{2} \sum_I \frac{1}{r_I^2} \left( 2 P_I^{(i} n_I^{j)} - (\delta^{ij} - n_I^i n_I^j) P_I^k n_I^k + \frac{4}{r_I} n_I^{(i} \epsilon^{j)kl} S_I^k n_I^l\right) \end{equation}
From it, we compute \(\alpha\) and \(\beta\) as:
\begin{align} \frac{1}{\alpha} &= \sum_I \frac{M_I}{2 r_I} \\ \beta &= \frac{1}{8} \alpha^7 \bar{A}_{ij} \bar{A}^{ij} \end{align}