Physics

This analysis thorn calculates the values of the Hamiltonian and momentum constraint equations on the computational grid during a spacetime evolution. The Hamiltonian Constraint (grid function: ham) is given by

$$H = R - K^{i}_{\;\;j} K^{j}_{\;\;i} + trK^2 - 16 \pi \rho$$ (part241)

The Momentum Constraints (grid functions momx, momy, momz) are given by

$$M_i = \nabla_j K_i^{\;\;j} - \nabla_i trK - 8 \pi S_i$$ (part242)

where

$$S_i = -g_{ia} n_b T^{ab} = - g_i^a n^b T_{ab} = -\frac{1}{\alpha} (T_{i0} - \beta^j T_{ij})$$ (part243)