Black-Hole Bombs and Photon-Mass Bounds

TL;DR

It is shown that massive vector fields around rotating black holes can give rise to a strong superradiant instability, which extracts angular momentum from the hole, and that current supermassive black-hole spin estimates provide the tightest upper limits on the mass of the photon.

Abstract

Generic extensions of the standard model predict the existence of ultralight bosonic degrees of freedom. Several ongoing experiments are aimed at detecting these particles or constraining their mass range. Here we show that massive vector fields around rotating black holes can give rise to a strong superradiant instability which extracts angular momentum from the hole. The observation of supermassive spinning black holes imposes limits on this mechanism. We show that current supermassive black hole spin estimates provide the tightest upper limits on the mass of the photon (mv<4x10^{-20} eV according to our most conservative estimate), and that spin measurements for the largest known supermassive black holes could further lower this bound to mv<10^{-22} eV. Our analysis relies on a novel framework to study perturbations of rotating Kerr black holes in the slow-rotation regime, that we developed up to second order in rotation, and that can be extended to other spacetime metrics and other theories.

Figures (2)

• Figure 1: Contour plots in the BH Regge plane Arvanitaki:2010sy corresponding to an instability timescale shorter than $\tau_{\rm Salpeter}$ for different values of the vector field mass $m_v={{\mu}}\hbar$ and for axial modes with $\ell=m=1$. Dashed lines bracket our estimated numerical errors, $\gamma_{01}\approx0.09\pm0.03$ in Eq. \ref{['fit_wI']}. The experimental points (with error bars) refer to the supermassive BHs listed in Table 2 of Brenneman:2011wz and the rightmost point corresponds to the supermassive BH in Fairall 9 Schmoll:2009gq. Supermassive BHs lying above each of these curves would be unstable on an observable timescale, and therefore each point rules out a range of Proca field masses.
• Figure 2: Comparison between axial and polar $\ell=m=1$ instability windows for $m_v=10^{-20}{\rm eV}$. The right boundary of the instability window does not depend on uncertainties in the fits and it is given by $J/M^2\equiv \tilde{a}\sim\tilde{a}_{\rm SR}\sim{4 M\mu}/{m}+{\cal O}(\mu^3)$, corresponding to the superradiance threshold [Eq. \ref{['superradiance']}] when $\omega_R\sim\mu$. For polar modes we show two different fitting functions. Fit I corresponds to Eq. \ref{['fit_wI']} with $\gamma_{-11}\approx20\pm10$, i.e, $M\omega_{I}=20({\tilde{a}}-2r_+\mu)(M\mu)^{7}$. Fit II is given by $M\omega_I\sim\left(\tilde{a} -\tilde{a}_{\rm SR}\right) \left[\eta_0(M\mu)^{\kappa_0}+\eta_1\tilde{a} (M\mu)^{\kappa_1}\right]$ with $\eta_0\approx-6.5\pm2$, $\eta_1\approx 2.1\pm1$, $\kappa_0\approx 6.0\pm0.1$, $\kappa_1\approx 5.0\pm0.3$. While fit I is physically more appealing Rosa:2011my, fit II does a better job at reproducing our numerical data in the whole instability region.