StrahlkorperGr Namespace Reference

Contains functions that depend both on a Strahlkorper and a metric. More...

## Namespaces

Tags
Holds tags and ComputeItems associated with a Strahlkorper that also need a metric.

## Functions

template<typename Frame >
tnsr::i< DataVector, 3, Frame > unit_normal_one_form (const tnsr::i< DataVector, 3, Frame > &normal_one_form, const DataVector &one_over_one_form_magnitude) noexcept
Computes normalized unit normal one-form to a Strahlkorper. More...

template<typename Frame >
tnsr::ii< DataVector, 3, Frame > grad_unit_normal_one_form (const tnsr::i< DataVector, 3, Frame > &r_hat, const DataVector &radius, const tnsr::i< DataVector, 3, Frame > &unit_normal_one_form, const tnsr::ii< DataVector, 3, Frame > &d2x_radius, const DataVector &one_over_one_form_magnitude, const tnsr::Ijj< DataVector, 3, Frame > &christoffel_2nd_kind) noexcept
Computes 3-covariant gradient $D_i S_j$ of a Strahlkorper's normal. More...

template<typename Frame >
tnsr::II< DataVector, 3, Frame > inverse_surface_metric (const tnsr::I< DataVector, 3, Frame > &unit_normal_vector, const tnsr::II< DataVector, 3, Frame > &upper_spatial_metric) noexcept
Computes inverse 2-metric $g^{ij}-S^i S^j$ of a Strahlkorper. More...

template<typename Frame >
Scalar< DataVectorexpansion (const tnsr::ii< DataVector, 3, Frame > &grad_normal, const tnsr::II< DataVector, 3, Frame > &inverse_surface_metric, const tnsr::ii< DataVector, 3, Frame > &extrinsic_curvature) noexcept
Expansion of a Strahlkorper. Should be zero on apparent horizons. More...

template<typename Frame >
tnsr::ii< DataVector, 3, Frame > extrinsic_curvature (const tnsr::ii< DataVector, 3, Frame > &grad_normal, const tnsr::i< DataVector, 3, Frame > &unit_normal_one_form, const tnsr::I< DataVector, 3, Frame > &unit_normal_vector) noexcept
Extrinsic curvature of a 2D Strahlkorper embedded in a 3D space. More...

template<typename Frame >
Scalar< DataVectorricci_scalar (const tnsr::ii< DataVector, 3, Frame > &spatial_ricci_tensor, const tnsr::I< DataVector, 3, Frame > &unit_normal_vector, const tnsr::ii< DataVector, 3, Frame > &extrinsic_curvature, const tnsr::II< DataVector, 3, Frame > &upper_spatial_metric) noexcept
Intrinsic Ricci scalar of a 2D Strahlkorper. More...

template<typename Frame >
Scalar< DataVectorarea_element (const tnsr::ii< DataVector, 3, Frame > &spatial_metric, const StrahlkorperTags::aliases::Jacobian< Frame > &jacobian, const tnsr::i< DataVector, 3, Frame > &normal_one_form, const DataVector &radius, const tnsr::i< DataVector, 3, Frame > &r_hat) noexcept
Area element of a 2D Strahlkorper. More...

template<typename Frame >
double surface_integral_of_scalar (const Scalar< DataVector > &area_element, const Scalar< DataVector > &scalar, const Strahlkorper< Frame > &strahlkorper) noexcept
Surface integral of a scalar on a 2D Strahlkorper More...

template<typename Frame >
Scalar< DataVectorspin_function (const StrahlkorperTags::aliases::Jacobian< Frame > &tangents, const YlmSpherepack &ylm, const tnsr::I< DataVector, 3, Frame > &unit_normal_vector, const Scalar< DataVector > &area_element, const tnsr::ii< DataVector, 3, Frame > &extrinsic_curvature) noexcept
Spin function of a 2D Strahlkorper. More...

template<typename Frame >
double dimensionful_spin_magnitude (const Scalar< DataVector > &ricci_scalar, const Scalar< DataVector > &spin_function, const tnsr::ii< DataVector, 3, Frame > &spatial_metric, const StrahlkorperTags::aliases::Jacobian< Frame > &tangents, const YlmSpherepack &ylm, const Scalar< DataVector > &area_element) noexcept
Spin magnitude measured on a 2D Strahlkorper. More...

template<typename Frame >
std::array< double, 3 > spin_vector (double spin_magnitude, const Scalar< DataVector > &area_element, const Scalar< DataVector > &radius, const tnsr::i< DataVector, 3, Frame > &r_hat, const Scalar< DataVector > &ricci_scalar, const Scalar< DataVector > &spin_function, const YlmSpherepack &ylm) noexcept
Spin vector of a 2D Strahlkorper. More...

double irreducible_mass (double area) noexcept
Irreducible mass of a 2D Strahlkorper. More...

## Detailed Description

Contains functions that depend both on a Strahlkorper and a metric.