Kerr-Newman metric
= Kerr-Newman metric
{c}
{title2=$\Delta=r^2-2Mr+a^2+Q^2,\quad a=J/M$}
{wiki=Kerr–Newman_metric}
= Kerr-Newman spacetime
{c}
{synonym}
The stationary axisymmetric Einstein–Maxwell family of <asymptotically flat spacetimes> extends the <Kerr metric> by including <electric charge>. Its horizon polynomial is the displayed $\Delta$; for $M^2>Q^2+a^2$ the roots are $r_\pm=M\pm\sqrt{M^2-Q^2-a^2}$. The outer <Killing horizon> has area $4\pi(r_+^2+a^2)$, angular velocity $a/(r_+^2+a^2)$ and electric potential $Qr_+/(r_+^2+a^2)$.