# DeSitter

### From GRwiki

The four-dimensional de Sitter space-time satisfies the Einstein equations in vacuum with a positive cosmological constant: . deSitter spacetime is the surface

where , in the five-dimensional flat spacetime

The surface can be covered with coordinates , , and , defined by

In these coordinates the deSitter metric is

#### Static coordinates

Let

The deSitter metric is

These coordinates cover only the strip of the full manifold. Let and the metric becomes

#### Conformally flat coordinates

Let

where . The metric is

Only the region is covered by these coordinates.