  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) + 2 n (N being the number of
supersymmetries and n the number of matter multiplets) and semipositive
definite.
