Non-BPS Black holes in N=4 Supersymmetric Yang-Mills Theory Coupled to Gravity

We construct non-BPS regular and black hole solutions of N=4 SU(N) supersymmetric Yang-Mills theory coupled to Einstein gravity. Our numerical studies reveal a number of interesting phenomena when the gravitational constant $\alpha =M_{YM}\mathrm{/}g{M}_{Planck}$ (where $M_{Planck}$ is the Planck mass and $M_{YM}$ is the monopole mass) is either weak (flat limit) or comparable to the Yang-Mills interaction. In fact, black hole solutions exist in a certain bounded domain in the $(\alpha ,r_H)$ plane where $r_H$ denotes the radius of the black