Imaginary charge on black hole I was wondering if one can put an imaginary charge on a black hole. What I mean is, take a Reissner-Nordstörm black hole and make the charge $Q$ and therefore also the imaginary potential pure imaginary by senden mu->i mu.
Has someone ever read a paper about that kind of stuff?
 A: If we set the charge of Reissner–Nordström soultion purely imaginary, the metric would be well defined:
$$ {\displaystyle {\rm {d}}s^{2}=\left(1-{\frac {r_{\rm {s}}}{r}}-{\frac {r_{\rm {Q}}^{2}}{r^{2}}}\right){\rm {d}}t^{2}-\left(1-{\frac {r_{\rm {s}}}{r}}-{\frac {r_{\rm {Q}}^{2}}{r^{2}}}\right)^{-1}{\rm {d}}r^{2}-r^{2}\,{\rm {d}}\Omega ^{2},}
$$where $r_{\rm s}=2M$, $r_{\rm Q}=|Q|^2$ (in units $G=c=k=1$).
 However, making the EM potential purely imaginary ($A=i |Q| / r \,\mathrm{d} t$) would make the energy of EM field negative and therefore the solution is unphysical. Therefore the geometry is rarely considered in literature. 
One exception is Andrew Hamilton's "proto-book" General Relativity, Black Holes, and Cosmology (pdf online) where he says the following (pp 202-203):

What makes the geometry interesting is that the singularity, instead of being gravitationally  repulsive,  becomes  gravitationally  attractive.  Thus  particles,  instead  of  bouncing  off  the
  singularity, are attracted to it, and it turns out to be possible to continue geodesics through the singularity.

