DBI equations and holographic DC conductivity

We provide a simple method for writing the Dirac-Born-Infeld (DBI) equations of a Dp-brane in an arbitrary static background whose metric depends only on the holographic radial coordinate z. Using this method we revisit the Karch-O'Bannon's procedure to calculate the DC conductivity in the presence of constant electric and magnetic fields for backgrounds where the boundary is four or three dimensional and satisfies homogeneity and isotropy. We find a frame-independent expression for the DC conductivity tensor. For particular backgrounds we recover previous results on holographic metals and strange metals.