Charged nutty black holes are hairy

TL;DR

The paper addresses how Misner-Dirac strings attached to charged nutty black holes can host observable electromagnetic hair. By treating the strings as physical singularities and employing a distributional analysis, the authors derive effective electric and magnetic charge densities along the strings, $\rho_e$ and $\rho_m$, and radius-dependent charges $Q(r)$ and $P(r)$ that reveal nonuniform flux entering the bulk. They classify hair patterns into SH, SS, and HH types, showing that rotation can generate horizon hair even without NUT, and that the horizon and string regions host sign-changing transition points that shape the lines of force. This framework demonstrates that MD strings are classically observable as short-range electromagnetic hair, connects with prior work on nutty spacetimes, and extends naturally to supergravity settings (EMDA), offering a practical lens to study black hole hair beyond traditional no-hair theorems.

Abstract

We uncover the physical nature of the electric and magnetic monopoles discovered by McGuire and Ruffini on Misner strings accompanying charged nutty black holes, showing that these strings carry singular, nonuniform flows of electric and magnetic fields. These fields inevitably have nonzero divergence, thereby simulating the effective electric and magnetic charge densities along the strings. The latter create a complex short-range electromagnetic hair zone around the horizon, making the combined Misner-Dirac strings classically observable. Typical features of this new type of hair are presented. We also note that rotation can act as a hair generator even in the absence of NUT.

Figures (17)

• Figure 1: Domain of integration for fluxes of electric and magnetic fields. (The arrows indicate the directions of the corresponding normal vectors.)
• Figure 2: $r_e<r_+$ ( $m=0.75,\; n=1.2,\; q=0.5,\; p=0$). Electric LFs start at the positively charged MD strings and at the horizon, spreading directly to infinity. Magnetic LFs are confined, starting form the horizon and closing on the MD strings (SH-hair).
• Figure 3: $r_e=r_+$ ($m=1,\; n=2,\; q=2,\; p=0$). Electric LFs propagate from the MD strings to infinity and not touching the horizon. Magnetic field is again of the SH hair type
• Figure 4: $r_e>r_+$ ($m=0.75,\; n=1.3,\; q=1.5,\; p=0$). The green circle $r=r_e$ separates the confined SH electric hair sector from the zone of LFs spreading to infinity. Magnetic hair now has both SH and SS sectors.
• Figure 5: $r_m<r_e<r_+$ ($m=2,\; n=1,\; q= p=0.71$). All the electric LFs starting either on the horizon or on the strings spread to infinity, while part of the magnetic LFs starting on the horizon end on Misner strings forming SH hair.