A Note on Exact Solutions and Attractor Mechanism for Non-BPS Black Holes

TL;DR

This paper presents two explicit extremal non-BPS black hole solutions in 4D supergravity, one with D2-D6 charges and the other with D0-D2-D4 charges, using a method based on assumed solution forms and duality transformations.

Contribution

It introduces new extremal non-BPS black hole solutions and demonstrates a method to derive them via assumed forms and duality transformations, linking to previous solutions.

Findings

Explicit D2-D6 non-BPS black hole solution obtained.

D0-D2-D4 solution derived through duality transformations.

Solutions are consistent with equations of motion and known dualities.

Abstract

We obtain two extremal, spherically symmetric, non-BPS black hole solutions to 4D supergravity, one of which carries D2-D6 charges and the other carries D0-D2-D4 charges. For the D2-D6 case, rather than solving the equations of motion directly, we assume the form of the solution and then find that the assumption satisfies the equations of motion and the constraint. Our D2-D6 solution is manifestly dual to the solution presented in 0710.4967. The D0-D2-D4 solution is obtained by performing certain $[SL(2,{\bf Z})]^{3}$ duality transformations on the D0-D4 solution in 0710.4967.