Many papers over the past 40 years discuss the magnetic moment and the $g$-factor of a black hole in the zeroth approximation and get the result $g=2$.
But what happens to the next approximation? Is the precise value
$g=2$ or $g= 2 + \alpha/\pi$ ?
Here $\alpha$ is the fine structure constant. Are there papers (I did not find any) or ideas on the issue? Will these values ever be tested in measurements?