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

TL;DR

This paper derives exact solutions for extremal non-BPS black holes in four-dimensional supergravity, revealing the attractor mechanism with complex moduli and identifying new parameters absent in previous solutions.

Contribution

It provides the first explicit exact solutions demonstrating the attractor mechanism for non-BPS black holes with complex moduli in supergravity.

Findings

Exact solutions exhibit the attractor mechanism for non-BPS black holes.

Moduli fields are complex, with an additional parameter not present in previous models.

Solutions generalize previous harmonic function approaches by including extra parameters.

Abstract

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.