Modified Palatini action that gives the Einstein-Maxwell theory

Understand

The actions for bosonic fields typically contain terms quadratic in the derivatives of the fields.

• This is not the case in the Palatini approach to general relativity.
• The action does not contain any derivatives of the metric and it only contains terms linear in the derivatives of the connection.
• In general relativity the covariant derivative of the metric vanishes, so it is not possible to include such terms in the action.