Can we live on a D-brane? Effective theory on a self-gravitating D-brane

We consider a D-brane coupled with gravity in type IIB supergravity on S-5 and derive the effective theory on the D-brane in two different ways: that is, holographic and geometrical projection methods. We find that the effective equations on the brane obtained by these methods coincide. The theory on the D-brane described by the Born-Infeld action is not like Einstein-Maxwell theory in the lower order of the gradient expansion; i.e., the Maxwell field does not appear in the theory. Thus a careful analysis and statement for cosmology on a self-gravitating D-brane should be demanded in realistic models.