SpECTRE
v2024.08.03

The conjugate momentum of the scalar field. More...
#include <Tags.hpp>
Public Types  
using  type = Scalar< DataVector > 
The conjugate momentum of the scalar field.
Its definition comes from requiring it to be the futuredirected time derivative of the scalar field \(\Psi\) in curved spacetime, see [166] , 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.