Rapid post-merger gravitational-wave signals from magnetic black hole superradiance: novel approach to detect magnetic monopole and ultralight boson

Abstract

We present an analytic framework showing that a spinning black hole with net magnetic charge exhibits a greatly enhanced superradiant instability against charged scalar fields compared with the neutral Kerr case. The enhancement arises from the monopole-induced reduction of the centrifugal barrier, $\ell(\ell+1)\to\ell(\ell+1)-q^2$, encoded by an effective quantum number $\ell_q$, with $q=eP=N/2$ fixed by Dirac quantization. This deepens the bound-state potential well and increases the instability growth rate. The resulting cloud can source near-monochromatic continuous gravitational waves (GWs). For a charged complex scalar, the stress tensor of a single monopole-harmonic sector is stationary, so the leading $2ω$ GW source instead arises from coherent north--south, equivalently charge-conjugate, cross terms. These select $(\tilde{\ell},\tilde{m},\tildeω)=(2q,+2q,+2ω)$ and its conjugate $(2q,-2q,-2ω)$. We find $P_{\rm GW}\propto(E_NE_S/M^2)α^{4\ell_q+8}$, or $P_{\rm GW}\propto(E_c/M)^2α^{4\ell_q+8}$ for a balanced cloud, rather than the neutral-Kerr scaling $α^{4\ell+10}$. This motivates prompt post-merger searches for magnetic monopoles and ultralight bosons. Unlike the Kerr case, where the signal turn-on may be delayed by years to centuries, a magnetic remnant can form a cloud and emit a stronger continuous signal within weeks to months. For $M\sim10^6M_\odot$, the signal can appear within weeks in the mHz band with strain $h\sim10^{-20}$.