The absolute (moduli-independent) U-invariants of all N > 2 extended supergravities at D = 4 are derived in terms of (moduli-dependent) central and matter charges. These invariants give a general definition of the topological Bekenstein-Hawking entropy formula for extremal black-holes and reduce to the square of the black-hole ADM mass for fixed scalars which extremize the black-hole potential energy. The Hessian matrix of the black-hole potential at fixed scalars , in contrast to N = 2 theories, is shown to be degenerate, with rank (N - 2) (N - 3) + 2n (N being the number of supersymmetries and n the number of matter multiplets) and semipositive definite.