E(7) symmetric area of the black hole horizon

Extreme black holes with $\frac{1}{8}$ of unbroken $N=8\mathrm{}$ supersymmetry are characterized by the nonvanishing area of the horizon. The central charge matrix has four generic eigenvalues. The area is proportional to the square root of the invariant quartic form of ${\mathrm{E}}_{7\left(7\right)\mathrm{}}$. It vanishes in all cases when ¼ or ½ of supersymmetry is unbroken. The supergravity nonrenormalization theorem for the area of the horizon in the $N=8\mathrm{}$ case protects the unique $U$-duality invariant.