= Magnetically charged dilaton black hole
{title2=$V=1-r_+/r,\quad R^2=r(r-r_-)$}
The unit-coupling magnetic solution of <Einstein-Maxwell-dilaton theory> has $ds^2=-Vdt^2+V^{-1}dr^2+R^2d\Omega_2^2$, magnetic potential $A=P\cos\theta\,d\phi$, and dilaton $\phi=-\tfrac12\log(1-r_-/r)$, where $r_-=2P^2/r_+$ and $r_+>0$. Its physical asymptotic component has $r>r_-$. For $0\le r_-<r_+$ it has a regular <Killing horizon> at $r_+$, area $4\pi r_+(r_+-r_-)$ and <surface gravity> $1/(2r_+)$. Its asymptotic mass is $r_+/2$. For $r_->r_+$ the zero-area singularity is naked. The limiting case $r_-=r_+$ is singular and must not be treated as a regular nondegenerate horizon.
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