Fourier-Mukai Transforms and Bridgeland Stability Conditions on Abelian Threefolds II

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.