Punctures::AnalyticData::MultiplePunctures Class Reference

Superposition of multiple punctures. More...

#include <MultiplePunctures.hpp>

Classes
struct	Punctures

Public Types
using	options = implementation defined

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"

Detailed Description

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:

$$\begin{array}{}\text{(1)}& {\overline{A}}^{ij}=\frac{3}{2}\sum _I\frac{1}{r_I^2}(2P_I^{(i}{n}_I^{j)}-({\delta }^{ij}-n_I^i{n}_I^j)P_I^k{n}_I^k+\frac{4}{r_I}{n}_I^{(i}{ϵ}^{j)kl}{S}_I^k{n}_I^l)\end{array}$$

From it, we compute $\alpha$ and $\beta$ as:

$$\begin{array}{}\text{(2)}& \frac{1}{\alpha }& =\sum _I\frac{M_I}{2r_I}\text{(3)}& \beta & =\frac{1}{8}{\alpha }^7{\overline{A}}_{ij}{\overline{A}}^{ij}\end{array}$$

See also

Punctures

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The documentation for this class was generated from the following file:

• src/PointwiseFunctions/AnalyticData/Punctures/MultiplePunctures.hpp