Light deflection in the gravimagnetic dipole spacetime

TL;DR

This work investigates gravitational lensing in the gravimagnetic dipole spacetime, a stationary, axisymmetric vacuum solution representing two equal-mass black holes with opposite NUT charges connected by a Misner string. It employs numerical null geodesics to compute equatorial-plane deflection and axial-lensing patterns, highlighting how the effective trajectories depend on the NUT parameter and separation. Key findings include zeros in the equatorial deflection indicating near-unperturbed passage between the holes and vertical-axial patterns showing both standard black-hole lensing and photons threading between the holes. The results expose rich lensing structures in multi-black-hole spacetimes with NUT charge and motivate further exploration of observational signatures of gravimagnetic configurations.

Abstract

The gravimagnetic dipole is an asymptotically flat, stationary, axisymmetric vacuum solution to Einstein's General Relativity describing two non-extreme black holes with equal masses and opposite NUT charges connected by a Misner string. The string tension's can be set to zero by choosing the black hole separation accordingly, yielding a stable system of oppositely rotating black holes at a fixed distance. Numerical simulations of massless particle geodesics reveal gravitational lensing effects for extended sources at infinity on the equatorial plane or on the vertical axis.

Figures (1)

• Figure 1: (a) Slice of the $XZ$ plane showing the black holes (orange dots), their horizons (dashed lines) and static limits (blue lines)ClementGMisner for $\nu = 0.4$ and $k \approx 1.575$. The real, positive $\alpha_\pm$ mark the horizon extremities on the $z$ axis. (b) Deflection angle as functions of $b$ for four different values of $\nu$. The singularity at $\rho =0$ appears as a discontinuity in $\Delta \phi$ near $b \approx -10$. For $\left\vert b\right\vert \gg k$, the curves resemble those for a single rotating black hole. Vertical asymptotes correspond to circular orbits. The zeros in $\Delta \phi$ correspond to photons that can pass between the black holes with their trajectory unaffected. (c) Deflection angle as a function of $\rho_{\hbox{init}}$ for four values of $\nu$. The rightmost part resembles single rotating black holes, the leftmost part shows that for $\nu$ large enough, photons can pass in between the black holes. (d) Zoom for $\nu = 0.8$. The zeros of $\Delta \phi$ indicate that photons can pass between the black holes and continue mostly unaffected. The markers refer to the trajectories depicted in (e). (e) Three example trajectories from (d). The blue circle and the orange square pass between the black holes then go to infinity, while the green diamond rotates in the $XY$ plane while curving around the upper black hole.