Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

Dilaton gravity from Chern–Simons gravity 139
The next term in the action (10), which is linear in the is the
standard one in the Kaluza–Klein approach and leads to
The final piece of the action (10) corresponds to a cosmological constant
term and is given by
Thus, the complete action (10) can be written as
In order to understand better the type of interaction produced by our
model it is more convenient to rewrite the above action (28) in terms of
components. The final reduced action reads, neglecting surface terms,