Stringy (Galilei) Newton-Hooke Chern-Simons Gravities

Understand

We construct Chern-Simons gravities in $(2+1)$-dimensional space-time considering the Stringy Galilei algebra both with and without non-central extensions.

• In the first case, there is an invariant and non-degenerate bilinear form, however, the field equations do not allow to express the spin connections in terms of the dreibeins.
• In the second case, there is no invariant non-degenerate bilinear form.
• Therefore, in both cases, we do not have an ordinary gravity theory.