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

Computes and returns spacetime quantities of interest. More...

#include <HarmonicSchwarzschild.hpp>

Public Types
using	CachedBuffer = HarmonicSchwarzschild::CachedBuffer<DataType, Frame>
Public Types inherited from CachedTempBuffer< internal_tags::x_minus_center< DataType, Frame >, internal_tags::r< DataType >, internal_tags::one_over_r< DataType >, internal_tags::x_over_r< DataType, Frame >, internal_tags::m_over_r< DataType >, internal_tags::sqrt_f_0< DataType >, internal_tags::f_0< DataType >, internal_tags::two_m_over_m_plus_r< DataType >, internal_tags::two_m_over_m_plus_r_squared< DataType >, internal_tags::two_m_over_m_plus_r_cubed< DataType >, internal_tags::spatial_metric_rr< DataType >, internal_tags::one_over_spatial_metric_rr< DataType >, internal_tags::spatial_metric_rr_minus_f_0< DataType >, internal_tags::d_spatial_metric_rr< DataType >, internal_tags::d_f_0< DataType >, internal_tags::d_f_0_times_x_over_r< DataType, Frame >, internal_tags::f_1< DataType >, internal_tags::f_1_times_x_over_r< DataType, Frame >, internal_tags::f_2< DataType >, internal_tags::f_2_times_xxx_over_r_cubed< DataType, Frame >, internal_tags::f_3< DataType >, internal_tags::f_4< DataType >, gr::Tags::Lapse< DataType >, internal_tags::neg_half_lapse_cubed_times_d_spatial_metric_rr< DataType >, gr::Tags::Shift< DataType, 3, Frame >, DerivShift< DataType, Frame >, gr::Tags::SpatialMetric< DataType, 3, Frame >, DerivSpatialMetric< DataType, Frame >, ::Tags::dt< gr::Tags::SpatialMetric< DataType, 3, Frame > >, gr::Tags::DetSpatialMetric< DataType >, internal_tags::one_over_det_spatial_metric< DataType > >
using	tags_list

Public Member Functions
tnsr::i< DataType, 3, Frame >	get_var (const IntermediateComputer< DataType, Frame > &computer, DerivLapse< DataType, Frame >)
	Computes and returns the spatial derivative of the lapse.
Scalar< DataType >	get_var (const IntermediateComputer< DataType, Frame > &computer, ::Tags::dt< gr::Tags::Lapse< DataType > >)
	Returns the time derivative of the lapse, which is 0.
tnsr::I< DataType, 3, Frame >	get_var (const IntermediateComputer< DataType, Frame > &computer, ::Tags::dt< gr::Tags::Shift< DataType, 3, Frame > >)
	Returns the time derivative of the shift, which is 0.
Scalar< DataType >	get_var (const IntermediateComputer< DataType, Frame > &computer, gr::Tags::SqrtDetSpatialMetric< DataType >)
	Computes and returns the square root of the determinant of the spatial metric.
tnsr::II< DataType, 3, Frame >	get_var (const IntermediateComputer< DataType, Frame > &computer, gr::Tags::InverseSpatialMetric< DataType, 3, Frame >)
	Computes and returns the inverse spatial metric.
tnsr::ii< DataType, 3, Frame >	get_var (const IntermediateComputer< DataType, Frame > &computer, gr::Tags::ExtrinsicCurvature< DataType, 3, Frame >)
	Computes and returns the extrinsic curvature.
const Tag::type &	get_var (const Computer &computer, Tag)
	Obtain a value from the buffer, computing it if necessary.
Public Member Functions inherited from CachedTempBuffer< internal_tags::x_minus_center< DataType, Frame >, internal_tags::r< DataType >, internal_tags::one_over_r< DataType >, internal_tags::x_over_r< DataType, Frame >, internal_tags::m_over_r< DataType >, internal_tags::sqrt_f_0< DataType >, internal_tags::f_0< DataType >, internal_tags::two_m_over_m_plus_r< DataType >, internal_tags::two_m_over_m_plus_r_squared< DataType >, internal_tags::two_m_over_m_plus_r_cubed< DataType >, internal_tags::spatial_metric_rr< DataType >, internal_tags::one_over_spatial_metric_rr< DataType >, internal_tags::spatial_metric_rr_minus_f_0< DataType >, internal_tags::d_spatial_metric_rr< DataType >, internal_tags::d_f_0< DataType >, internal_tags::d_f_0_times_x_over_r< DataType, Frame >, internal_tags::f_1< DataType >, internal_tags::f_1_times_x_over_r< DataType, Frame >, internal_tags::f_2< DataType >, internal_tags::f_2_times_xxx_over_r_cubed< DataType, Frame >, internal_tags::f_3< DataType >, internal_tags::f_4< DataType >, gr::Tags::Lapse< DataType >, internal_tags::neg_half_lapse_cubed_times_d_spatial_metric_rr< DataType >, gr::Tags::Shift< DataType, 3, Frame >, DerivShift< DataType, Frame >, gr::Tags::SpatialMetric< DataType, 3, Frame >, DerivSpatialMetric< DataType, Frame >, ::Tags::dt< gr::Tags::SpatialMetric< DataType, 3, Frame > >, gr::Tags::DetSpatialMetric< DataType >, internal_tags::one_over_det_spatial_metric< DataType > >
	CachedTempBuffer (const size_t size)
	Construct the buffer with the given computer. size is passed to the underlying TempBuffer constructor.
const Tag::type &	get_var (const Computer &computer, Tag)
	Obtain a value from the buffer, computing it if necessary.
size_t	number_of_grid_points () const

Detailed Description

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

Computes and returns spacetime quantities of interest.

Member Function Documentation

get_var()

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

tnsr::i< DataType, 3, Frame > gr::Solutions::HarmonicSchwarzschild::IntermediateVars< DataType, Frame >::get_var	(	const IntermediateComputer< DataType, Frame > &	computer,
		DerivLapse< DataType, Frame >	)

Computes and returns the spatial derivative of the lapse.

Details

Computed as

\begin{align} \partial_i \alpha &= -\frac{1}{2} \gamma_{rr}^{-3/2} \partial_r \gamma_{rr} \frac{X_i}{r} \end{align}

where \(r\) is the radius defined by internal_tags::r, \(\gamma_{rr}\) is defined by internal_tags::spatial_metric_rr, its derivative \(\partial_r \gamma_{rr}\) is defined by internal_tags::d_spatial_metric_rr, 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