Rapid post-merger signal of circularly polarized gravitational wave from magnetic black hole superradiance: novel approach to detect magnetic monopole

TL;DR

The paper shows that a magnetically charged black hole dramatically modifies charged-scalar superradiance by replacing the centrifugal barrier with an effective ℓ_q, yielding ω_I ∝ α^{4ℓ_q+5} and much faster growth than in Kerr. This leads to macroscopic, hemispherically localized clouds that emit near-monochromatic GWs with enhanced power and a distinctive helicity pattern from north/south clouds, producing approximately circular polarization at fixed sky locations. The authors derive the analytic growth-rate scaling via a matched-asymptotic treatment and compute the GW power, including a self-consistent BH–cloud evolution that accounts for GW depletion, making concrete predictions for rapid post-merger GW signals in the mHz to Hz bands and a polarization-based smoking-gun test for magnetic monopoles. Together, these results provide a self-contained framework for observational strategies to detect magnetic monopoles through circularly polarized gravitational waves from magnetically charged black-hole remnants.

Abstract

We present an analytic framework demonstrating that a spinning black hole endowed with a net magnetic charge exhibits a dramatically amplified superradiant instability against charged scalar fields, enhanced by several orders of magnitude compared with the neutral Kerr case. The amplification arises from a monopole induced reduction of the centrifugal barrier. This shift deepens the gravitational bound-state potential well and produces a parametrically larger instability growth rate. This resulting rapid growth yields a macroscopic boson cloud that acts as a coherent source of near monochromatic continuous gravitational waves (GWs). We find an enhanced GW power. Monopole harmonic selection rules restrict the emission from the north (south) clouds corresponding to opposite helicities. Their superposition generates an (approximately) circularly polarized continuous GWs at a fixed sky location within even parity general relativity, distinct from the generic elliptical polarization of the Kerr case. In light of these new findings, we propose a potential smoking-gun search strategy for magnetic monopole and ultralight boson: the rapid post-merger follow-up GW signals from binary-black-hole merger remnants through ground-based and space-based GW experiments. In contrast to the Kerr case, where the signal turn-on can be delayed to decades-centuries, a magnetic remnant can form a cloud and emit a stronger, circularly polarized continuous GWs within weeks to months. Taking the magnetic supermassive remnants as an example, we demonstrate that the rapid follow-up GW signal in the mHz band appears just in few weeks after binary black hole mergers. Moreover, future polarization (ellipticity) measurements can distinguish the magnetic scenario from Kerr while providing a parity-even mechanism for circularly polarized GWs in general relativity.

Figures (8)

• Figure 1: Schematic illustration of helicity-polarized GW emission from hemispherically localized charged scalar clouds around a magnetically charged black hole. Angular-momentum selection rules imply that the north cloud in the $m=+q$ mode radiates GWs dominantly in $(\tilde{\ell},\tilde{m})=(2q,+2q)$, while the south cloud in the $m=-q$ mode radiates in $(\tilde{\ell},\tilde{m})=(2q,-2q)$, producing opposite GW helicities in the two hemispheres.
• Figure 2: Normalized GW power $P_{\rm GW}(\alpha)/(E_{c}/M)^2$ for the dominant annihilation channel. Top: neutral Kerr (211, 322) versus charged clouds with $\ell=q$ for representative $q$. Bottom: north $(+)$ versus south $(-)$ branches; the convergence at larger $q$ reflects the emergent north--south symmetry.
• Figure 3: GW strain from boson clouds around a rotating black hole with $M=10^6 M_\odot$. Left: neutral case ($\alpha=0.3$, $\mu\simeq 4.0\times 10^{-17}\,$eV), dominated by a single mode, yielding elliptical polarization and a beat in $|h|$. Right: magnetic case ($\alpha=0.45$, $\mu\simeq 6.0\times 10^{-17}\,$eV), where north/south monopole-harmonic clouds populate opposite-helicity modes $(\tilde{\ell},\tilde{m})=(2q,\pm 2q)$; their superposition gives near-circular polarization with an almost constant envelope. Top: short-window waveforms $h_+=\Re[h]$, $h_\times=-\Im[h]$, and $|h|$. Middle/bottom: strain envelope and instantaneous frequency $f_{\rm GW}(t)$ during cloud growth and depletion.
• Figure S1: Schematic meridional ($x$--$z$) slice of the cloud profile built from the maximally unstable monopole-harmonic modes $Y^{+}_{qqq}$ (north) and $Y^{-}_{qq,-q}$ (south).
• Figure S3: Analytical growth rate $M\omega_I$ of charged scalar clouds around a magnetic BH as a function of $\alpha\equiv\mu M$. Solid (dashed) curves correspond to $a/M=0.9$ ($a/M=0.7$). We take the fundamental radial mode $n_r=0$ and set $P/M\sim10^{-19}$. Colors label the monopole number: black/blue/orange/purple denote $N=0,1,2,3$, respectively. For $N=0$, we take $\ell=m=1$. For $N\ge1$, we take $\ell=m=q=N/2$ with $\ell_q=\sqrt{(\ell+1/2)^2-q^2}-1/2$. The analytical results agree with the numerical values of Ref. Pereniguez:2024fkn to within an order of magnitude.