gr::Solutions::HarmonicSchwarzschild::IntermediateComputer< DataType, Frame > Class Template Reference

Computes the intermediates and quantities that we do not want to recompute across the solution's implementation. More...

#include <HarmonicSchwarzschild.hpp>

Public Types
using	CachedBuffer = HarmonicSchwarzschild::CachedBuffer< DataType, Frame >

Public Member Functions
	IntermediateComputer (const HarmonicSchwarzschild &solution, const tnsr::I< DataType, 3, Frame > &x)
	Constructs a computer for spacetime quantities of a given gr::Solutions::HarmonicSchwarzschild solution at at a specific Cartesian position. More...
void	operator() (gsl::not_null< tnsr::I< DataType, 3, Frame > * > x_minus_center, gsl::not_null< CachedBuffer * >, internal_tags::x_minus_center< DataType, Frame >) const
	Computes the intermediate defined by internal_tags::x_minus_center
void	operator() (gsl::not_null< Scalar< DataType > * > r, gsl::not_null< CachedBuffer * > cache, internal_tags::r< DataType >) const
	Computes the radius defined by internal_tags::r
void	operator() (gsl::not_null< Scalar< DataType > * > one_over_r, gsl::not_null< CachedBuffer * > cache, internal_tags::one_over_r< DataType >) const
	Computes the intermediate defined by internal_tags::one_over_r
void	operator() (gsl::not_null< tnsr::I< DataType, 3, Frame > * > x_over_r, gsl::not_null< CachedBuffer * > cache, internal_tags::x_over_r< DataType, Frame >) const
	Computes the intermediate defined by internal_tags::x_over_r
void	operator() (gsl::not_null< Scalar< DataType > * > m_over_r, gsl::not_null< CachedBuffer * > cache, internal_tags::m_over_r< DataType >) const
	Computes the intermediate defined by internal_tags::m_over_r
void	operator() (gsl::not_null< Scalar< DataType > * > sqrt_f_0, gsl::not_null< CachedBuffer * > cache, internal_tags::sqrt_f_0< DataType >) const
	Computes the intermediate defined by internal_tags::sqrt_f_0
void	operator() (gsl::not_null< Scalar< DataType > * > f_0, gsl::not_null< CachedBuffer * > cache, internal_tags::f_0< DataType >) const
	Computes the intermediate defined by internal_tags::f_0
void	operator() (gsl::not_null< Scalar< DataType > * > two_m_over_m_plus_r, gsl::not_null< CachedBuffer * > cache, internal_tags::two_m_over_m_plus_r< DataType >) const
	Computes the intermediate defined by internal_tags::two_m_over_m_plus_r
void	operator() (gsl::not_null< Scalar< DataType > * > two_m_over_m_plus_r_squared, gsl::not_null< CachedBuffer * > cache, internal_tags::two_m_over_m_plus_r_squared< DataType >) const
	Computes the intermediate defined by internal_tags::two_m_over_m_plus_r_squared
void	operator() (gsl::not_null< Scalar< DataType > * > two_m_over_m_plus_r_cubed, gsl::not_null< CachedBuffer * > cache, internal_tags::two_m_over_m_plus_r_cubed< DataType >) const
	Computes the intermediate defined by internal_tags::two_m_over_m_plus_r_cubed
void	operator() (gsl::not_null< Scalar< DataType > * > spatial_metric_rr, gsl::not_null< CachedBuffer * > cache, internal_tags::spatial_metric_rr< DataType >) const
	Computes the intermediate defined by internal_tags::spatial_metric_rr
void	operator() (gsl::not_null< Scalar< DataType > * > one_over_spatial_metric_rr, gsl::not_null< CachedBuffer * > cache, internal_tags::one_over_spatial_metric_rr< DataType >) const
	Computes the intermediate defined by internal_tags::one_over_spatial_metric_rr
void	operator() (gsl::not_null< Scalar< DataType > * > spatial_metric_rr_minus_f_0, gsl::not_null< CachedBuffer * > cache, internal_tags::spatial_metric_rr_minus_f_0< DataType >) const
	Computes the intermediate defined by internal_tags::spatial_metric_rr_minus_f_0
void	operator() (gsl::not_null< Scalar< DataType > * > d_spatial_metric_rr, gsl::not_null< CachedBuffer * > cache, internal_tags::d_spatial_metric_rr< DataType >) const
	Computes the intermediate defined by internal_tags::d_spatial_metric_rr
void	operator() (gsl::not_null< Scalar< DataType > * > d_f_0, gsl::not_null< CachedBuffer * > cache, internal_tags::d_f_0< DataType >) const
	Computes the intermediate defined by internal_tags::d_f_0
void	operator() (gsl::not_null< tnsr::i< DataType, 3, Frame > * > d_f_0_times_x_over_r, gsl::not_null< CachedBuffer * > cache, internal_tags::d_f_0_times_x_over_r< DataType, Frame >) const
	Computes the intermediate defined by internal_tags::d_f_0_times_x_over_r
void	operator() (gsl::not_null< Scalar< DataType > * > f_1, gsl::not_null< CachedBuffer * > cache, internal_tags::f_1< DataType >) const
	Computes the intermediate defined by internal_tags::f_1
void	operator() (gsl::not_null< tnsr::i< DataType, 3, Frame > * > f_1_times_x_over_r, gsl::not_null< CachedBuffer * > cache, internal_tags::f_1_times_x_over_r< DataType, Frame >) const
	Computes the intermediate defined by internal_tags::f_1_times_x_over_r
void	operator() (gsl::not_null< Scalar< DataType > * > f_2, gsl::not_null< CachedBuffer * > cache, internal_tags::f_2< DataType >) const
	Computes the intermediate defined by internal_tags::f_2
void	operator() (gsl::not_null< tnsr::iii< DataType, 3, Frame > * > f_2_times_xxx_over_r_cubed, gsl::not_null< CachedBuffer * > cache, internal_tags::f_2_times_xxx_over_r_cubed< DataType, Frame >) const
	Computes the intermediate defined by internal_tags::f_2_times_xxx_over_r_cubed
void	operator() (gsl::not_null< Scalar< DataType > * > f_3, gsl::not_null< CachedBuffer * > cache, internal_tags::f_3< DataType >) const
	Computes the intermediate defined by internal_tags::f_3
void	operator() (gsl::not_null< Scalar< DataType > * > f_4, gsl::not_null< CachedBuffer * > cache, internal_tags::f_4< DataType >) const
	Computes the intermediate defined by internal_tags::f_4
void	operator() (gsl::not_null< Scalar< DataType > * > lapse, gsl::not_null< CachedBuffer * > cache, gr::Tags::Lapse< DataType >) const
	Computes the lapse. More...
void	operator() (gsl::not_null< Scalar< DataType > * > neg_half_lapse_cubed_times_d_spatial_metric_rr, gsl::not_null< CachedBuffer * > cache, internal_tags::neg_half_lapse_cubed_times_d_spatial_metric_rr< DataType >) const
	Computes the intermediate defined by internal_tags::neg_half_lapse_cubed_times_d_spatial_metric_rr
void	operator() (gsl::not_null< tnsr::I< DataType, 3, Frame > * > shift, gsl::not_null< CachedBuffer * > cache, gr::Tags::Shift< DataType, 3, Frame >) const
	Computes the shift. More...
void	operator() (gsl::not_null< tnsr::iJ< DataType, 3, Frame > * > deriv_shift, gsl::not_null< CachedBuffer * > cache, DerivShift< DataType, Frame >) const
	Computes the spatial derivative of the shift. More...
void	operator() (gsl::not_null< tnsr::ii< DataType, 3, Frame > * > spatial_metric, gsl::not_null< CachedBuffer * > cache, gr::Tags::SpatialMetric< DataType, 3, Frame >) const
	Computes the spatial metric. More...
void	operator() (gsl::not_null< tnsr::ijj< DataType, 3, Frame > * > deriv_spatial_metric, gsl::not_null< CachedBuffer * > cache, DerivSpatialMetric< DataType, Frame >) const
	Computes the spatial derivative of the spatial metric. More...
void	operator() (gsl::not_null< tnsr::ii< DataType, 3, Frame > * > dt_spatial_metric, gsl::not_null< CachedBuffer * > cache, ::Tags::dt< gr::Tags::SpatialMetric< DataType, 3, Frame > >) const
	Sets the time derivative of the spatial metric to 0.
void	operator() (gsl::not_null< Scalar< DataType > * > det_spatial_metric, gsl::not_null< CachedBuffer * > cache, gr::Tags::DetSpatialMetric< DataType >) const
	Computes the determinant of the spatial metric.
void	operator() (gsl::not_null< Scalar< DataType > * > one_over_det_spatial_metric, gsl::not_null< CachedBuffer * > cache, internal_tags::one_over_det_spatial_metric< DataType >) const
	Computes one over the determinant of the spatial metric.

Detailed Description

template<typename DataType, typename Frame = ::Frame::Inertial>
class gr::Solutions::HarmonicSchwarzschild::IntermediateComputer< DataType, Frame >

Computes the intermediates and quantities that we do not want to recompute across the solution's implementation.

Constructor & Destructor Documentation

IntermediateComputer()

template<typename DataType , typename Frame = ::Frame::Inertial>

gr::Solutions::HarmonicSchwarzschild::IntermediateComputer< DataType, Frame >::IntermediateComputer	(	const HarmonicSchwarzschild &	solution,
		const tnsr::I< DataType, 3, Frame > &	x
	)

Constructs a computer for spacetime quantities of a given gr::Solutions::HarmonicSchwarzschild solution at at a specific Cartesian position.

Parameters

solution	the given gr::Solutions::HarmonicSchwarzschild solution
x	Cartesian coordinates of the position at which to compute spacetime quantities

Member Function Documentation

operator()() [1/5]

template<typename DataType , typename Frame = ::Frame::Inertial>

void gr::Solutions::HarmonicSchwarzschild::IntermediateComputer< DataType, Frame >::operator()	(	gsl::not_null< Scalar< DataType > * >	lapse,
		gsl::not_null< CachedBuffer * >	cache,
		gr::Tags::Lapse< DataType >
	)		const

Computes the lapse.

Details

Computed as

$$\begin{array}{}\text{(1)}& \alpha & ={\gamma }_{rr}^{-1/2}\end{array}$$

where ${\gamma }_{rr}$ is a component of the spatial metric defined by internal_tags::spatial_metric_rr.

operator()() [2/5]

template<typename DataType , typename Frame = ::Frame::Inertial>

void gr::Solutions::HarmonicSchwarzschild::IntermediateComputer< DataType, Frame >::operator()	(	gsl::not_null< tnsr::I< DataType, 3, Frame > * >	shift,
		gsl::not_null< CachedBuffer * >	cache,
		gr::Tags::Shift< DataType, 3, Frame >
	)		const

Computes the shift.

Details

Computed as

$$\begin{array}{}\text{(2)}& {\beta }^i& ={\left(\frac{2M}{M+r}\right)}^2\frac{X^i}{r}\frac{1}{{\gamma }_{rr}}\end{array}$$

where $M$ is the mass of the black hole, $r$ is the radius defined by internal_tags::r, $X^i$ is defined by internal_tags::x_minus_center, and ${\gamma }_{rr}$ is defined by internal_tags::spatial_metric_rr.

operator()() [3/5]

template<typename DataType , typename Frame = ::Frame::Inertial>

void gr::Solutions::HarmonicSchwarzschild::IntermediateComputer< DataType, Frame >::operator()	(	gsl::not_null< tnsr::ii< DataType, 3, Frame > * >	spatial_metric,
		gsl::not_null< CachedBuffer * >	cache,
		gr::Tags::SpatialMetric< DataType, 3, Frame >
	)		const

Computes the spatial metric.

Details

Computed as

$$\begin{array}{}\text{(3)}& {\gamma }_{ij}& =({\gamma }_{rr}-{(1+\frac{M}{r})}^2)\frac{X_i}{r}\frac{X_j}{r}+{\delta }_{ij}{(1+\frac{M}{r})}^2\end{array}$$

where $M$ is the mass of the black hole, $r$ is the radius defined by internal_tags::r, ${\gamma }_{rr}$ is defined by internal_tags::spatial_metric_rr, and $X_j=X^i{\delta }_{ij}$ where $X^i$ is defined by internal_tags::x_minus_center.

operator()() [4/5]

template<typename DataType , typename Frame = ::Frame::Inertial>

void gr::Solutions::HarmonicSchwarzschild::IntermediateComputer< DataType, Frame >::operator()	(	gsl::not_null< tnsr::iJ< DataType, 3, Frame > * >	deriv_shift,
		gsl::not_null< CachedBuffer * >	cache,
		DerivShift< DataType, Frame >
	)		const

Computes the spatial derivative of the shift.

Details

Computed as

$$\begin{array}{}\text{(4)}& {\partial }_k{\beta }^i& =f_4\frac{X^i}{r}\frac{X_k}{r}+{\delta }_k^i{f}_3\end{array}$$

where $r$ is the radius defined by internal_tags::r, $X^i$ is defined by internal_tags::x_minus_center, $X_j=X^i{\delta }_{ij}$, $f_3$ is defined by internal_tags::f_3, and $f_4$ is defined by internal_tags::f_4.

operator()() [5/5]

template<typename DataType , typename Frame = ::Frame::Inertial>

void gr::Solutions::HarmonicSchwarzschild::IntermediateComputer< DataType, Frame >::operator()	(	gsl::not_null< tnsr::ijj< DataType, 3, Frame > * >	deriv_spatial_metric,
		gsl::not_null< CachedBuffer * >	cache,
		DerivSpatialMetric< DataType, Frame >
	)		const

Computes the spatial derivative of the spatial metric.

Details

Computed as

$$\begin{array}{}\text{(5)}& {\partial }_k{\gamma }_{ij}& =f_2\frac{X_i}{r}\frac{X_j}{r}\frac{X_k}{r}+f_1\frac{X_j}{r}{\delta }_{ik}+f_1\frac{X_i}{r}{\delta }_{jk}+{\partial }_r{f}_0\frac{X_k}{r}{\delta }_{ij}\end{array}$$

where $r$ is the radius defined by internal_tags::r, ${\partial }_r{f}_0$ is defined by internal_tags::d_f_0, $f_1$ is defined by internal_tags::f_1, $f_2$ 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.

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

• src/PointwiseFunctions/AnalyticSolutions/GeneralRelativity/HarmonicSchwarzschild.hpp