SpECTRE  v2022.09.02
CurvedScalarWave::Tags::Pi Struct Reference

The conjugate momentum of the scalar field. More...

#include <Tags.hpp>

## Public Types

using type = Scalar< DataVector >

## Detailed Description

The conjugate momentum of the scalar field.

### Details

Its definition comes from requiring it to be the future-directed time derivative of the scalar field $$\Psi$$ in curved spacetime, see [112] , Eq. 2.16:

\begin{align} \Pi :=& -n^a \partial_a \Psi \\ =& \frac{1}{\alpha}\left(\beta^k \partial_k \Psi - {\partial_t\Psi}\right),\\ \end{align}

where $$n^a$$ is the unit normal to spatial slices of the spacetime foliation, $$\alpha$$ is the lapse and $$\beta^i$$ is the shift vector.

The documentation for this struct was generated from the following file:
• src/Evolution/Systems/CurvedScalarWave/Tags.hpp