A field theoretic approach to the energy momentum tensor for theories coupled with gravity

We provide a field-theoretic algorithm of obtaining energy momentum tensor (EMT) for gravitationally coupled theories. The method is based on an auxiliary field theory and equally applicable to both minimal and non-minimal coupling. The algorithm illuminates the connection between the EMT, obtained by functional variation of the metric, and local balance of energy and momentum. Our method is of cardinal value for the proper identification of the EMT in context of non-minimally coupled gravity theories.