Vacua and Exact Solutions in Lower-$D$ Limits of EGB

Understand

We consider the action principles that are the lower dimensional limits of the Einstein-Gauss-Bonnet gravity {\it via} the Kaluza-Klein route.

• We study the vacua and obtain some exact solutions.
• We find that the reality condition of the theories may select one vacuum over the other from the two vacua that typically arise in Einstein-Gauss-Bonnet gravity.
• We obtain exact black hole and cosmological solutions carrying scalar hair, including scalar hairy BTZ black holes with both mass and angular momentum turned on.