SpECTRE
v2024.05.11
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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 = tmpl::list< Tags... > |
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 |
Computes and returns spacetime quantities of interest.
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.
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
.