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 $2\omega$ GW source instead arises from coherent north--south, equivalently charge-conjugate, cross terms. These select $(\tilde{\ell },\tilde{m},\tilde{\omega })=(2q,+2q,+2\omega )$ and its conjugate $(2q,-2q,-2\omega )$. We find $P_{\mathrm{GW}}\propto (E_N{E}_S/M^2){\alpha }^{4{\ell }_q+8}$, or $P_{\mathrm{GW}}\propto (E_c/M{)}^2{\alpha }^{4{\ell }_q+8}$ for a balanced cloud, rather than the neutral-Kerr scaling ${\alpha }^{4\ell +10}$. 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 $M\sim 10^6{M}_{\odot }$, the signal can appear within weeks in the mHz band with strain $h\sim 10^{-20}$.

Comments: 38 pages, 7 figures; comments are welcome