# Einstein Equations

### From GRwiki

Let denote Newton's constant. The Einstein equations are

where is the Einstein tensor and is the stress-energy-momentum tensor. These equations extremize the action

where is the determinant of the spacetime metric and is the spacetime curvature scalar. The matter fields are denoted collectively by . The stress-energy-momentum tensor is obtained from the matter action by

Formulations of the Einstein equations include:

- Hamiltonian (ADM)
- gdot-Kdot
- BSSN
- Generalized BSSN
- KST
- NOR
- Generalized Harmonic (second order)
- Generalized Harmonic (first order)