Holds functions related to general relativity. More...
Namespaces | |
| Solutions | |
| Classes which implement analytic solutions to Einstein's equations. | |
Classes | |
| class | KerrSchildCoords |
| Contains helper functions for transforming tensors in Kerr spacetime to Kerr-Schild coordinates. More... | |
Functions | |
| template<size_t SpatialDim, typename Frame , IndexType Index, typename DataType > | |
| void | christoffel_first_kind (const gsl::not_null< tnsr::abb< DataType, SpatialDim, Frame, Index > *> christoffel, const tnsr::abb< DataType, SpatialDim, Frame, Index > &d_metric) noexcept |
| template<size_t Dim, typename Frame , typename DataType > | |
| void | spacetime_metric (const gsl::not_null< tnsr::aa< DataType, Dim, Frame > *> spacetime_metric, const Scalar< DataType > &lapse, const tnsr::I< DataType, Dim, Frame > &shift, const tnsr::ii< DataType, Dim, Frame > &spatial_metric) noexcept |
| template<size_t Dim, typename Frame , typename DataType > | |
| tnsr::aa< DataType, Dim, Frame > | spacetime_metric (const Scalar< DataType > &lapse, const tnsr::I< DataType, Dim, Frame > &shift, const tnsr::ii< DataType, Dim, Frame > &spatial_metric) noexcept |
| template<size_t SpatialDim, typename Frame , typename DataType > | |
| tnsr::ii< DataType, SpatialDim, Frame > | spatial_metric (const tnsr::aa< DataType, SpatialDim, Frame > &spacetime_metric) noexcept |
| Compute spatial metric from spacetime metric. More... | |
| template<size_t Dim, typename Frame , typename DataType > | |
| tnsr::AA< DataType, Dim, Frame > | inverse_spacetime_metric (const Scalar< DataType > &lapse, const tnsr::I< DataType, Dim, Frame > &shift, const tnsr::II< DataType, Dim, Frame > &inverse_spatial_metric) noexcept |
| template<size_t SpatialDim, typename Frame , typename DataType > | |
| tnsr::I< DataType, SpatialDim, Frame > | shift (const tnsr::aa< DataType, SpatialDim, Frame > &spacetime_metric, const tnsr::II< DataType, SpatialDim, Frame > &inverse_spatial_metric) noexcept |
| Compute shift from spacetime metric and inverse spatial metric. More... | |
| template<size_t SpatialDim, typename Frame , typename DataType > | |
| Scalar< DataType > | lapse (const tnsr::I< DataType, SpatialDim, Frame > &shift, const tnsr::aa< DataType, SpatialDim, Frame > &spacetime_metric) noexcept |
| Compute lapse from shift and spacetime metric. More... | |
| template<size_t Dim, typename Frame , typename DataType > | |
| tnsr::abb< DataType, Dim, Frame > | derivatives_of_spacetime_metric (const Scalar< DataType > &lapse, const Scalar< DataType > &dt_lapse, const tnsr::i< DataType, Dim, Frame > &deriv_lapse, const tnsr::I< DataType, Dim, Frame > &shift, const tnsr::I< DataType, Dim, Frame > &dt_shift, const tnsr::iJ< DataType, Dim, Frame > &deriv_shift, const tnsr::ii< DataType, Dim, Frame > &spatial_metric, const tnsr::ii< DataType, Dim, Frame > &dt_spatial_metric, const tnsr::ijj< DataType, Dim, Frame > &deriv_spatial_metric) noexcept |
| template<size_t SpatialDim, typename Frame , typename DataType > | |
| tnsr::a< DataType, SpatialDim, Frame > | spacetime_normal_one_form (const Scalar< DataType > &lapse) noexcept |
| Computes spacetime normal one-form from lapse. More... | |
| template<size_t SpatialDim, typename Frame , typename DataType > | |
| tnsr::A< DataType, SpatialDim, Frame > | spacetime_normal_vector (const Scalar< DataType > &lapse, const tnsr::I< DataType, SpatialDim, Frame > &shift) noexcept |
| Computes spacetime normal vector from lapse and shift. More... | |
| template<size_t SpatialDim, typename Frame , typename DataType > | |
| tnsr::ii< DataType, SpatialDim, Frame > | extrinsic_curvature (const Scalar< DataType > &lapse, const tnsr::I< DataType, SpatialDim, Frame > &shift, const tnsr::iJ< DataType, SpatialDim, Frame > &deriv_shift, const tnsr::ii< DataType, SpatialDim, Frame > &spatial_metric, const tnsr::ii< DataType, SpatialDim, Frame > &dt_spatial_metric, const tnsr::ijj< DataType, SpatialDim, Frame > &deriv_spatial_metric) noexcept |
| Computes extrinsic curvature from metric and derivatives. More... | |
| template<size_t SpatialDim, typename Frame , typename DataType > | |
| tnsr::AA< DataType, SpatialDim, Frame > | inverse_spacetime_metric (const Scalar< DataType > &lapse, const tnsr::I< DataType, SpatialDim, Frame > &shift, const tnsr::II< DataType, SpatialDim, Frame > &inverse_spatial_metric) noexcept |
| Compute inverse spacetime metric from inverse spatial metric, lapse and shift. More... | |
| template<size_t SpatialDim, typename Frame , typename DataType > | |
| tnsr::abb< DataType, SpatialDim, Frame > | derivatives_of_spacetime_metric (const Scalar< DataType > &lapse, const Scalar< DataType > &dt_lapse, const tnsr::i< DataType, SpatialDim, Frame > &deriv_lapse, const tnsr::I< DataType, SpatialDim, Frame > &shift, const tnsr::I< DataType, SpatialDim, Frame > &dt_shift, const tnsr::iJ< DataType, SpatialDim, Frame > &deriv_shift, const tnsr::ii< DataType, SpatialDim, Frame > &spatial_metric, const tnsr::ii< DataType, SpatialDim, Frame > &dt_spatial_metric, const tnsr::ijj< DataType, SpatialDim, Frame > &deriv_spatial_metric) noexcept |
| Computes spacetime derivative of spacetime metric from spatial metric, lapse, shift, and their space and time derivatives. More... | |
| bool | operator!= (const KerrSchildCoords &lhs, const KerrSchildCoords &rhs) noexcept |
| template<size_t SpatialDim, typename Frame , IndexType Index, typename DataType > | |
| tnsr::aa< DataType, SpatialDim, Frame, Index > | ricci_tensor (const tnsr::Abb< DataType, SpatialDim, Frame, Index > &christoffel_2nd_kind, const tnsr::aBcc< DataType, SpatialDim, Frame, Index > &d_christoffel_2nd_kind) noexcept |
| Computes Ricci tensor from the (spatial or spacetime) Christoffel symbol of the second kind and its derivative. More... | |
| template<size_t SpatialDim, typename Frame , IndexType Index, typename DataType > | |
| tnsr::abb< DataType, SpatialDim, Frame, Index > | christoffel_first_kind (const tnsr::abb< DataType, SpatialDim, Frame, Index > &d_metric) noexcept |
| Computes Christoffel symbol of the first kind from derivative of metric. More... | |
| template<size_t SpatialDim, typename Frame , IndexType Index, typename DataType > | |
| void | christoffel_first_kind (gsl::not_null< tnsr::abb< DataType, SpatialDim, Frame, Index > *> christoffel, const tnsr::abb< DataType, SpatialDim, Frame, Index > &d_metric) noexcept |
| Computes Christoffel symbol of the first kind from derivative of metric. More... | |
| template<size_t Dim, typename Frame , typename DataType > | |
| void | spacetime_metric (gsl::not_null< tnsr::aa< DataType, Dim, Frame > *> spacetime_metric, const Scalar< DataType > &lapse, const tnsr::I< DataType, Dim, Frame > &shift, const tnsr::ii< DataType, Dim, Frame > &spatial_metric) noexcept |
| Computes the spacetime metric from the spatial metric, lapse, and shift. More... | |
| template<size_t SpatialDim, typename Frame , typename DataType > | |
| tnsr::aa< DataType, SpatialDim, Frame > | spacetime_metric (const Scalar< DataType > &lapse, const tnsr::I< DataType, SpatialDim, Frame > &shift, const tnsr::ii< DataType, SpatialDim, Frame > &spatial_metric) noexcept |
| Computes the spacetime metric from the spatial metric, lapse, and shift. More... | |
Holds functions related to general relativity.
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noexcept |
Computes spacetime normal one-form from lapse.
If \(N\) is the lapse, then
\begin{align} n_t &= - N \\ n_i &= 0 \end{align}
is computed.