Exact Solutions and the Attractor Mechanism in Non-BPS Black Holes

The attractor mechanism for the four-dimensional ${\cal N}=2$ supergravity black hole solution is analyzed in the case of the D0-D4 system. Our analyses are based on newly derived exact solutions, which exhibit explicitly the attractor mechanism for extremal non-BPS black holes. Our solutions account for the moduli as general complex fields, while in almost all non-BPS solutions obtained previously, the moduli fields are restricted to be purely imaginary. It is also pointed out that our moduli solutions contain an extra parameter that is not contained in solutions obtained by replacing the charges in the double extremal moduli solutions by the corresponding harmonic functions.