Superradiant scattering of electromagnetic fields from ringing black holes

TL;DR

The paper studies EM wave scattering from a ringing Schwarzschild black hole (BH) during its ringdown, showing that the EM absorption cross section can exhibit transient superradiance driven by the oscillating gravitational background. To handle the time-dependent spacetime, the authors introduce a hypothetical interaction surface that allows a well-defined, region-separated calculation of the absorption cross section, and they compute a mean cross section by averaging over the surface location. They develop a perturbative framework with gauge-invariant EM variables, reveal how GW quasinormal modes (QNM) imprint on the EM field through mode coupling, and solve for the resulting nonholmogeneous EM dynamics, demonstrating time-dependent amplification on GW timescales with a calculable energy extraction and brightness-temperature signature. Numerically, they show maximum amplification at a finite interaction radius and identify frequency cutoffs $ ext{k}_{ m max}$ that depend on angular momentum $l$; for primordial black holes (PBHs) with masses $M ext{ in the range }10^{-1}-10^{-2}M_ ext{odot}$, the transient EM signal could lie in the LOFAR band, offering a potential electromagnetic probe of PBH-PBH mergers. The work thus provides a novel EM signature of BH ringdowns and opens a path to multimessenger observations of PBH mergers in radio bands.

Abstract

Detection of gravitational waves (GWs) paves the beginning of a new era of gravitational wave astronomy. Black holes (BHs) in their ringdown phase provide the cleanest signal of emitted GWs that imprint the fundamental nature of BHs under low energy perturbation. Apart from GWs, any complementary signature of ringing BHs can be of paramount importance. Motivated by this we analyzed the scattering of electromagnetic waves in such a background and demonstrated that the absorption cross section of a ringing Schwarzschild BH can be superradiant. Moreover, we have found out that such superradiant phenomena are transient in nature with a characteristic time scale equal to the GW oscillation time scale. We further point out that the existing ground-based Low Frequency Array (LOFAR), radio telescopes, may be able to detect such transient signals from BHs of mass range $M\sim 10^{-1} - 10^{-2} M_{\odot}$, which should necessarily be of primordial origin. Our present result opens up an intriguing possibility of observing the black hole merging phenomena through electromagnetic waves.

Figures (7)

• Figure 1: We demonstrate the inclusion of the hypothetical interaction surface in the ringing black hole spacetime. Shaded region (${\bf I}$) is considered as the spacetime containing ringing fluctuations and outside region $({\bf II})$ is considered as the usual Schwarzschild spacetime.
• Figure 2: On the left panel absorption cross section of the ringing BH for the EM field has been plotted with time, $u$, for various interaction surfaces, $r_{int}$, considering frequency, $\mathrm{k}=0.1 r^{-1}_h$ and $l=1$. On the right panel, we have plotted the same by varying the background amplitude, $\mathcal{E}_h, \mathcal{O}_h$, considering frequency, $\mathrm{k}=0.1 r^{-1}_h$ and $l=1$ at a particular interaction surface $r_{int}=20 r_h$. All the parameters written inside the plots are in units of $r_h$.
• Figure 3: On the left panel absorption cross section of the ringing black hole for the EM field has been plotted with time, $u$, by varying the frequency, $\mathrm{k}$, of the EM field considering $l=1$. On the right panel, we have plotted the same various angular modes, $l$, of the EM field considering $\mathrm{k}=0.1 r^{-1}_h$. All the parameters written inside the plots are in units of $r_h$.
• Figure 4: Mean absorption cross section has been plotted with time by averaging over the position of the interaction surface, $r_{\rm int}$ for a fixed frequency, $\mathrm{k}=0.1 r^{-1}_h$ and $l=1$.
• Figure 5: Schematic diagram of the BH merging phase, illustrating a scenario where the BH masses and initial configuration are chosen such that the quiescence time occurs in the current era of the universe. An incoming photon from a Pulsar or Quasar, intended as a target source for LOFAR, may scatter off the ringing black hole and undergo amplification.