  We show that the conjectural construction proposed by Bayer, Bertram, Macr\'i
and Toda gives rise to Bridgeland stability conditions for a principally
polarized abelian three-fold with Picard rank one by proving that tilt stable
objects satisfy the strong Bogomolov-Gieseker type inequality. This is done by
showing any Fourier-Mukai transform gives an equivalence of abelian categories
which are double tilts of coherent sheaves.
