First-order framework for flat brane with auxiliary fields
  This work deals with braneworld models in the presence of auxiliary fields. We investigate the case where Einstein's equation is modified with the inclusion of extra, non-dynamical terms. We show that the model supports first-order differential equations that solve the equations of motion, but the standard braneworld scenario changes under the presence of the parameter that controls the non-dynamical or auxiliary fields that modifies Einstein's equation. 
D. Bazeia, A. S. Lob\~ao Jr., R. Menezes
hep-th hep-ph