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SpECTRE
v2024.04.12
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Tags defined for intermediates specific to the harmonic Schwarzschild solution. More...
#include <HarmonicSchwarzschild.hpp>
Public Types | |
| template<typename DataType , typename Frame = ::Frame::Inertial> | |
| using | x_minus_center = ::Tags::TempI< 0, 3, Frame, DataType > |
| Tag for the position of a point relative to the center of the black hole. More... | |
| template<typename DataType > | |
| using | r = ::Tags::TempScalar< 1, DataType > |
| Tag for the radius corresponding to the position of a point relative to the center of the black hole. More... | |
| template<typename DataType > | |
| using | one_over_r = ::Tags::TempScalar< 2, DataType > |
| Tag for one over the radius corresponding to the position of a point relative to the center of the black hole. More... | |
| template<typename DataType , typename Frame = ::Frame::Inertial> | |
| using | x_over_r = ::Tags::TempI< 3, 3, Frame, DataType > |
| Tag for the intermediate \(\frac{X^i}{r}\). More... | |
| template<typename DataType > | |
| using | m_over_r = ::Tags::TempScalar< 4, DataType > |
| Tag for the intermediate \(\frac{M}{r}\). More... | |
| template<typename DataType > | |
| using | sqrt_f_0 = ::Tags::TempScalar< 5, DataType > |
| Tag for the intermediate \(\sqrt{f_0} = 1 + \frac{M}{r}\). More... | |
| template<typename DataType > | |
| using | f_0 = ::Tags::TempScalar< 6, DataType > |
| Tag for the intermediate \(f_0 = \left(1 + \frac{M}{r}\right)^2\). More... | |
| template<typename DataType > | |
| using | two_m_over_m_plus_r = ::Tags::TempScalar< 7, DataType > |
| Tag for the intermediate \(\frac{2M}{M+r}\). More... | |
| template<typename DataType > | |
| using | two_m_over_m_plus_r_squared = ::Tags::TempScalar< 8, DataType > |
| Tag for the intermediate \(\left(\frac{2M}{M+r}\right)^2\). More... | |
| template<typename DataType > | |
| using | two_m_over_m_plus_r_cubed = ::Tags::TempScalar< 9, DataType > |
| Tag for the intermediate \(\left(\frac{2M}{M+r}\right)^3\). More... | |
| template<typename DataType > | |
| using | spatial_metric_rr = ::Tags::TempScalar< 10, DataType > |
| Tag for the \(\gamma_{rr}\) component of the spatial metric. More... | |
| template<typename DataType > | |
| using | one_over_spatial_metric_rr = ::Tags::TempScalar< 11, DataType > |
| Tag for the intermediate \(\frac{1}{\gamma_{rr}}\). More... | |
| template<typename DataType > | |
| using | spatial_metric_rr_minus_f_0 = ::Tags::TempScalar< 12, DataType > |
| Tag for the intermediate \(\gamma_{rr} - f_0\). More... | |
| template<typename DataType > | |
| using | d_spatial_metric_rr = ::Tags::TempScalar< 13, DataType > |
| Tag for the intermediate \(\partial_r \gamma_{rr}\). More... | |
| template<typename DataType > | |
| using | d_f_0 = ::Tags::TempScalar< 14, DataType > |
| Tag for the intermediate \(\partial_r f_0\). More... | |
| template<typename DataType , typename Frame = ::Frame::Inertial> | |
| using | d_f_0_times_x_over_r = ::Tags::Tempi< 15, 3, Frame, DataType > |
| Tag for the intermediate \(\partial_r f_0 \frac{X_i}{r}\). More... | |
| template<typename DataType > | |
| using | f_1 = ::Tags::TempScalar< 16, DataType > |
| Tag for the intermediate \(f_1 = \frac{1}{r} \left(\gamma_{rr} - f_0\right)\). More... | |
| template<typename DataType , typename Frame = ::Frame::Inertial> | |
| using | f_1_times_x_over_r = ::Tags::Tempi< 17, 3, Frame, DataType > |
| Tag for the intermediate \(f_1 \frac{X_i}{r}\). More... | |
| template<typename DataType > | |
| using | f_2 = ::Tags::TempScalar< 18, DataType > |
| Tag for the intermediate \(f_2 = \partial_r \gamma_{rr} - \partial_r f_0 - 2 f_1\). More... | |
| template<typename DataType , typename Frame = ::Frame::Inertial> | |
| using | f_2_times_xxx_over_r_cubed = ::Tags::Tempiii< 19, 3, Frame, DataType > |
| Tag for the intermediate \(f_2 \frac{X_i}{r} \frac{X_j}{r} \frac{X_k}{r}\). More... | |
| template<typename DataType > | |
| using | f_3 = ::Tags::TempScalar< 20, DataType > |
| Tag for the intermediate \(f_3 = \frac{1}{r}\frac{1}{\gamma_{rr}}\left(\frac{2M}{M+r}\right)^2\). More... | |
| template<typename DataType > | |
| using | f_4 = ::Tags::TempScalar< 21, DataType > |
| Tag for the intermediate. More... | |
| template<typename DataType > | |
| using | one_over_det_spatial_metric = ::Tags::TempScalar< 22, DataType > |
| Tag for one over the determinant of the spatial metric. | |
| template<typename DataType > | |
| using | neg_half_lapse_cubed_times_d_spatial_metric_rr = ::Tags::TempScalar< 23, DataType > |
| Tag for the intermediate \(-\frac{1}{2} \gamma_{rr}^{-3/2} \partial_r \gamma_{rr}\). More... | |
Tags defined for intermediates specific to the harmonic Schwarzschild solution.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::d_f_0 = ::Tags::TempScalar<14, DataType> |
Tag for the intermediate \(\partial_r f_0\).
Defined as
\begin{align} \partial_r f_0 &= 2 \left(1+\frac{M}{r}\right)\left(-\frac{M}{r^2}\right) \end{align}
where \(M\) is the mass of the black hole and \(r\) is the radius defined by internal_tags::r.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::d_f_0_times_x_over_r = ::Tags::Tempi<15, 3, Frame, DataType> |
Tag for the intermediate \(\partial_r f_0 \frac{X_i}{r}\).
The quantity \(r\) is the radius defined by internal_tags::r, \(\partial_r f_0\) is defined by internal_tags::d_f_0, and \(X_j = X^i \delta_{ij}\) where \(X^i\) is defined by internal_tags::x_minus_center.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::d_spatial_metric_rr = ::Tags::TempScalar<13, DataType> |
Tag for the intermediate \(\partial_r \gamma_{rr}\).
Defined as
\begin{align} \partial_r \gamma_{rr} &= -\frac{1}{2M}\left(\frac{2M}{M+r}\right)^2 -\frac{1}{M}\left(\frac{2M}{M+r}\right)^3 -\frac{3}{2M}\left(\frac{2M}{M+r}\right)^4 \end{align}
where \(M\) is the mass of the black hole and \(r\) is the radius defined by internal_tags::r.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::f_0 = ::Tags::TempScalar<6, DataType> |
Tag for the intermediate \(f_0 = \left(1 + \frac{M}{r}\right)^2\).
The quantity \(M\) is the mass of the black hole and \(r\) is the radius defined by internal_tags::r.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::f_1 = ::Tags::TempScalar<16, DataType> |
Tag for the intermediate \(f_1 = \frac{1}{r} \left(\gamma_{rr} - f_0\right)\).
The quantity \(r\) is the radius defined by internal_tags::r, \(\gamma_{rr}\) is defined by internal_tags::spatial_metric_rr, and \(f_0\) is defined by internal_tags::f_0.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::f_1_times_x_over_r = ::Tags::Tempi<17, 3, Frame, DataType> |
Tag for the intermediate \(f_1 \frac{X_i}{r}\).
The quantity \(r\) is the radius defined by internal_tags::r, \(f_1\) is defined by internal_tags::f_1, and \(X_j = X^i \delta_{ij}\) where \(X^i\) is defined by internal_tags::x_minus_center.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::f_2 = ::Tags::TempScalar<18, DataType> |
Tag for the intermediate \(f_2 = \partial_r \gamma_{rr} - \partial_r f_0 - 2 f_1\).
The quantity \(\partial_r \gamma_{rr}\) is defined by internal_tags::d_spatial_metric_rr, \(\partial_r f_0\) is defined by internal_tags::d_f_0, and \(f_1\) is defined by internal_tags::f_1.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::f_2_times_xxx_over_r_cubed = ::Tags::Tempiii<19, 3, Frame, DataType> |
Tag for the intermediate \(f_2 \frac{X_i}{r} \frac{X_j}{r} \frac{X_k}{r}\).
The quantity \(r\) is the radius defined by internal_tags::r, \(f_2\) is defined by internal_tags::f_2, and \(X_j = X^i \delta_{ij}\) where \(X^i\) is defined by internal_tags::x_minus_center.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::f_3 = ::Tags::TempScalar<20, DataType> |
Tag for the intermediate \(f_3 = \frac{1}{r}\frac{1}{\gamma_{rr}}\left(\frac{2M}{M+r}\right)^2\).
The quantity \(M\) is the mass of the black hole, \(r\) is the radius defined by internal_tags::r, and \(\gamma_{rr}\) is defined by internal_tags::spatial_metric_rr.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::f_4 = ::Tags::TempScalar<21, DataType> |
Tag for the intermediate.
\begin{align} f_4 &= -f_3 - \frac{1}{M} \frac{1}{\gamma_{rr}} \left(\frac{2M}{M+r}\right)^3 - \partial_r \gamma_{rr} \left(\frac{2 M}{M+r} \frac{1}{\gamma_{rr}}\right)^2 \end{align}
The quantity \(M\) is the mass of the black hole, \(r\) is the radius defined by internal_tags::r, \(f_3\) is defined by internal_tags::f_3, \(\gamma_{rr}\) is defined by internal_tags::spatial_metric_rr, and its derivative \(\partial_r \gamma_{rr}\) is defined by internal_tags::d_spatial_metric_rr.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::m_over_r = ::Tags::TempScalar<4, DataType> |
Tag for the intermediate \(\frac{M}{r}\).
The quantity \(M\) is the mass of the black hole and \(r\) is the radius defined by internal_tags::r.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::neg_half_lapse_cubed_times_d_spatial_metric_rr = ::Tags::TempScalar<23, DataType> |
Tag for the intermediate \(-\frac{1}{2} \gamma_{rr}^{-3/2} \partial_r \gamma_{rr}\).
The lapse is defined as \(\alpha = \gamma_{rr}^{-1/2}\), \(\gamma_{rr}\) is defined by internal_tags::spatial_metric_rr and its derivative \(\partial_r \gamma_{rr}\) is defined by internal_tags::d_spatial_metric_rr.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::one_over_r = ::Tags::TempScalar<2, DataType> |
Tag for one over the radius corresponding to the position of a point relative to the center of the black hole.
The quantity \(r\) is the radius defined by internal_tags::r.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::one_over_spatial_metric_rr = ::Tags::TempScalar<11, DataType> |
Tag for the intermediate \(\frac{1}{\gamma_{rr}}\).
The quantity \(\gamma_{rr}\) is defined by internal_tags::spatial_metric_rr.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::r = ::Tags::TempScalar<1, DataType> |
Tag for the radius corresponding to the position of a point relative to the center of the black hole.
Defined as \(r = \sqrt{\delta_{ij} X^i X^j}\), where \(X^i\) is defined by internal_tags::x_minus_center.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::spatial_metric_rr = ::Tags::TempScalar<10, DataType> |
Tag for the \(\gamma_{rr}\) component of the spatial metric.
Defined as
\begin{align} \gamma_{rr} &= 1 + \frac{2M}{M+r} + \left(\frac{2M}{M+r}\right)^2 + \left(\frac{2M}{M+r}\right)^3 \end{align}
where \(M\) is the mass of the black hole and \(r\) is the radius defined by internal_tags::r.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::spatial_metric_rr_minus_f_0 = ::Tags::TempScalar<12, DataType> |
Tag for the intermediate \(\gamma_{rr} - f_0\).
The quantity \(\gamma_{rr}\) is defined by internal_tags::spatial_metric_rr and \(f_0\) is defined by internal_tags::f_0.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::sqrt_f_0 = ::Tags::TempScalar<5, DataType> |
Tag for the intermediate \(\sqrt{f_0} = 1 + \frac{M}{r}\).
The quantity \(M\) is the mass of the black hole, \(r\) is the radius defined by internal_tags::r, and \(f_0\) is defined by internal_tags::f_0.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::two_m_over_m_plus_r = ::Tags::TempScalar<7, DataType> |
Tag for the intermediate \(\frac{2M}{M+r}\).
The quantity \(M\) is the mass of the black hole and \(r\) is the radius defined by internal_tags::r.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::two_m_over_m_plus_r_cubed = ::Tags::TempScalar<9, DataType> |
Tag for the intermediate \(\left(\frac{2M}{M+r}\right)^3\).
The quantity \(M\) is the mass of the black hole and \(r\) is the radius defined by internal_tags::r.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::two_m_over_m_plus_r_squared = ::Tags::TempScalar<8, DataType> |
Tag for the intermediate \(\left(\frac{2M}{M+r}\right)^2\).
The quantity \(M\) is the mass of the black hole and \(r\) is the radius defined by internal_tags::r.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::x_minus_center = ::Tags::TempI<0, 3, Frame, DataType> |
Tag for the position of a point relative to the center of the black hole.
Defined as \(X^i = \left(x^i - C^i\right)\), where \(C^i\) is the Cartesian coordinates of the center of the black hole and \(x^i\) is the Cartesian coordinates of the point where we're wanting to compute spacetime quantities.
| using gr::Solutions::HarmonicSchwarzschild::internal_tags::x_over_r = ::Tags::TempI<3, 3, Frame, DataType> |
Tag for the intermediate \(\frac{X^i}{r}\).
The quantity \(X^i\) is defined by internal_tags::x_minus_center and \(r\) is the radius defined by internal_tags::r.