Binary Black Holes’ Effects on Electromagnetic Fields

In addition to producing gravitational waves, the dynamics of a binary black hole system could induce emission of electromagnetic radiation by affecting the behavior of plasmas and electromagnetic fields in their vicinity. We here study how the electromagnetic fields are affected by a pair of orbiting black holes through the merger. In particular, we show how the binary’s dynamics induce a variability in possible electromagnetically induced emissions as well as a possible enhancement of electromagnetic fields during the late-merge and merger epochs. These time dependent features will likely leave their imprint in processes generating detectable emissions and can be exploited in the detection of electromagnetic counterparts of gravitational waves.

Figure 1

The electric field for $y=0$, $z\ge 0$ at $t=200M$ for a single black hole, together with the apparent horizon (lower curve) and the ergosphere (upper curve). The region $x<0$ displays the numerical solution, while Wald’s exact solution is $x>0$.

Figure 2

Magnetic and electric field lines at $t\simeq -40M$, $-20M$ in 3D (the merger happens at $t=0$). The electric field lines are twisted around the black hole, while the magnetic lines are mostly aligned with the $z$ axis.

Figure 3

The radial component of the Poynting vector for the binary black hole case. The structure reveals it is dominated by (spherical harmonic) $\mathrm{EM}{c}_{0,0}$ and $\mathrm{EM}{c}_{2,0}$ modes in the orbiting stage though close to merger a $\mathrm{EM}{c}_{2,2}$ is induced which lags behind the corresponding gravitational wave (spin-2 spherical harmonic) $\mathrm{GW}{c}_{2,2}$. The transient behavior before $t\simeq -100$ is spurious and due to the initial data employed.

Figure 4

Normalized electromagnetic energy density (with respect to its value at the initial time in the absence of black holes). The first and second row correspond to $y=0$ and $z=0$, respectively, at times $t\simeq -70$, 5, and $30M$. The last row corresponds to the single black hole case at $t=150M$ for the sake of comparison. Normalized energy contour plots are shown with lines from 1.2 to 0.8 at intervals of 0.1. Around the merger epoch, the energy computed for the binary case is $\simeq 30\%–40\%$ larger than in the single case.