Can Light Cross a Singularity? Exact Solutions from Analogue Gravity

Abstract

Using a simple spacetime hosting a strong curvature naked singularity, we employ an analogue gravity model to study electromagnetic fields in this background. We find exact solutions to the full set of electrostatic and electrodynamic equations that remain regular even in the presence of the singularity. Moreover, certain solutions sustain a regular and bounded power flux across the singularity, suggesting that electromagnetic energy may be transmitted through it.

Figures (6)

• Figure 1: Global structure of the spacetime given by Eq. \ref{['mettoy-1']}. Some timelike geodesics are shown in red. The wavy black curve is the naked, timelike singularity at $x=0$.
• Figure 2: Trajectories of light in the $x-y$ plane according to GO; these are null geodesics of the spacetime.
• Figure 3: Vector plot of the electrostatic field in a two-dimensional case. Increasing values from blue to red.
• Figure 4: Electrostatic energy density in the same case as in Fig. \ref{['fig:electrostatic_field']}. Increasing values from blue to red.
• Figure 5: Time-averaged Poynting vector for one case with $c^2+{k_y}^2\neq0$. Increasing values from blue to red.