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< Tags >
using	tags_list = implementation defined

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. More...
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.
template<typename Computer , typename Tag >
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< Tags >
	CachedTempBuffer (const size_t size)
	Construct the buffer with the given computer. size is passed to the underlying TempBuffer constructor.
template<typename Computer , typename Tag >
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

$$\begin{array}{}\text{(1)}& {\partial }_i\alpha & =-\frac{1}{2}{\gamma }_{rr}^{-3/2}{\partial }_r{\gamma }_{rr}\frac{X_i}{r}\end{array}$$

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