SpECTRE  v2022.06.14
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 [111] , 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: