SpECTRE  v2024.03.19
gr::AnalyticData::BrillLindquist::internal_tags Struct Reference

Tags defined for intermediates specific to BrillLindquist data. More...

#include <BrillLindquist.hpp>

Public Types

template<typename DataType , typename Frame >
using x_minus_center_a = ::Tags::TempI< 0, 3, Frame, DataType >
 Tag for the position of a point relative to the center of black hole A. More...
 
template<typename DataType >
using r_a = ::Tags::TempScalar< 1, DataType >
 Tag for the radius corresponding to the position of a point relative to the center of black hole A. More...
 
template<typename DataType , typename Frame >
using x_minus_center_b = ::Tags::TempI< 2, 3, Frame, DataType >
 Tag for the position of a point relative to the center of black hole B. More...
 
template<typename DataType >
using r_b = ::Tags::TempScalar< 3, DataType >
 Tag for the radius corresponding to the position of a point relative to the center of black hole B. More...
 
template<typename DataType >
using conformal_factor = ::Tags::TempScalar< 4, DataType >
 Tag for the conformal factor. More...
 
template<typename DataType , typename Frame >
using deriv_conformal_factor = ::Tags::Tempi< 5, 3, Frame, DataType >
 Tag for the deriatives of the conformal factor. More...
 

Detailed Description

Tags defined for intermediates specific to BrillLindquist data.

Member Typedef Documentation

◆ conformal_factor

Tag for the conformal factor.

Details

Defined as \(\psi = 1 + \frac{m_A}{2 r_A} + \frac{m_B}{2 r_B}\) where \(m_{A,B}\) are the masses of the black holes and \(r_{A,B}\) are the positions of a point relative to the center of each black hole

◆ deriv_conformal_factor

template<typename DataType , typename Frame >
using gr::AnalyticData::BrillLindquist::internal_tags::deriv_conformal_factor = ::Tags::Tempi<5, 3, Frame, DataType>

Tag for the deriatives of the conformal factor.

Details

Defined as \(d_i\psi = -\frac{m_A X_A^j}{2 r_A^3} \delta_{ij} - \frac{m_B X_B^j}{2 r_B^3} \delta_{ij}\) where \(m_{A,B}\) are the masses of the black holes and \(r_{A,B}\) are the positions of a point relative to the center of each black hole. (Note we are free to raise/lower coordinate indices with a Eucledian metric)

◆ r_a

template<typename DataType >
using gr::AnalyticData::BrillLindquist::internal_tags::r_a = ::Tags::TempScalar<1, DataType>

Tag for the radius corresponding to the position of a point relative to the center of black hole A.

Details

Defined as \(r_A = \sqrt{\delta_{ij} X_A^i X_A^j}\), where \(X_A^i\) is defined by internal_tags::x_minus_center_a.

◆ r_b

template<typename DataType >
using gr::AnalyticData::BrillLindquist::internal_tags::r_b = ::Tags::TempScalar<3, DataType>

Tag for the radius corresponding to the position of a point relative to the center of black hole B.

Details

Defined as \(r_B = \sqrt{\delta_{ij} X_B^i X_B^j}\), where \(X_B^i\) is defined by internal_tags::x_minus_center_b.

◆ x_minus_center_a

template<typename DataType , typename Frame >
using gr::AnalyticData::BrillLindquist::internal_tags::x_minus_center_a = ::Tags::TempI<0, 3, Frame, DataType>

Tag for the position of a point relative to the center of black hole A.

Details

Defined as \(X_A^i = \left(x^i - C_A^i\right)\), where \(C_A^i\) is the Cartesian coordinates of the center of black hole A and \(x^i\) is the Cartesian coordinates of the point where we're wanting to compute spacetime quantities.

◆ x_minus_center_b

template<typename DataType , typename Frame >
using gr::AnalyticData::BrillLindquist::internal_tags::x_minus_center_b = ::Tags::TempI<2, 3, Frame, DataType>

Tag for the position of a point relative to the center of black hole B.

Details

Defined as \(X_B^i = \left(x^i - C_B^i\right)\), where \(C_B^i\) is the Cartesian coordinates of the center of black hole B and \(x^i\) is the Cartesian coordinates of the point where we're wanting to compute spacetime quantities.


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