Overview

The CactusEinstein arrangement provides a suite of thorns for doing numerical relativity simulations. The basic variables are those of the ADM formulation of Einstein's equations, namely the spatial 3-metric $\gamma_{ij}$, the lapse $\alpha$, the shift $\beta$, and the extrinsic curvature $K_{ij}$. The 4-metric is given by

$$ds^2 = -(\alpha^2 - \beta^i \beta_i) dt^2 + \beta_i dt dx^i + \gamma_{ij} dx^i dx^j \;.$$

If $\gamma_{ij}$ is the 3-metric of a spacelike Cauchy surface with normal $n$, then

$$K_{ij} = \frac{1}{2}{\cal L}_n \gamma_{ij} \;.$$

These variables are defined in the thorn ADMBase, and are the ones that are used to communicate the geometry to other thorns. It is not necessary to use these as the basic variables of your computation, however. All you need do is compute these quantities at each iteration in order to communicate with the CactusEinstein thorns.

There are a number of initial data thorns, an ADM thorn for evolution, and thorns which provide many other pieces of infrastructure. It is not necessary to use all of these thorns to make use of CactusEinstein, however. The only thorn which is necessary is ADMBase, since it defines the variables and parameters on which the rest of the CactusEinstein thorns depend.