Can the graviton have a large mass near black holes?

The mass of the graviton, if nonzero, is usually considered to be very small, e.g., of the Hubble scale, from several observational constraints. In this paper, we propose a gravity model where the graviton mass is very small in the usual weak gravity environments, below all the current graviton mass bounds, but becomes much larger in the strong gravity regime such as a black hole’s vicinity. For black holes in this model, significant deviations from general relativity emerge very close to the black hole horizon and alter the black hole quasinormal modes, which can be extracted from the ringdown wave form of black hole binary mergers. Also, the enhancement of the graviton mass near the horizon can result in echoes in the late-time ringdown, which can be verified in the upcoming gravitational wave observations of higher sensitivity.

Figure 1

Numerical black hole solutions. The parameters chosen are $m_{\sigma }={10}^{-2}m$, $k_3=-1/10$, ${\alpha }_3=-2/k_3$, ${\alpha }_4=3/k_3^2$ and ${\lambda }_{\sigma }=0$. $A$ is the $tt$ metric component, $V^{1/2}$ is the graviton mass and $r_g=2G{M}_{\mathrm{bh}}$.

Figure 2

Deviations from GR for geodesics near black holes. We choose $k_3=-1/10$ and ${\lambda }_{\sigma }=0$. The contours depict fractional deviations (0.1%, 1% and 10%) of the relevant quantities from their GR counterparts.

Figure 3

Power spectral density of the GW signals sourced by two $30M_{\odot }$ black holes inspiraling in a circular orbit at a distance of 410 Mpc. The frequencies are cut off at a separation of $3r_g$. The gray dashed line is for GR, while the blue and orange lines are for MVMG with $m{r}_g=7.4$ and $m{r}_g=40.8$ respectively ($m_{\sigma }/m={10}^{-2.25}$). The solid black line shows the design sensitivity of advanced LIGO.

Figure 4

The upper panel shows the effective potential $U_{\mathrm{eff}}$ with $l=2$ against the tortoise coordinate $r_{*}$ in GR (gray dashed line) and MVMG (orange solid line). The lower panel shows the wave forms of a test scalar wave packet scattered in GR (gray dashed line) and MVMG (orange solid line) black hole background. The orange dashed line shows the difference between the GR and MVMG wave forms, which are echoes caused by the extra barrier in MVMG. The wave packet has the initial configuration Eq. (6) with $r_0=5r_g$ and $r_{\sigma }=3r_g$. For MVMG, we choose $m_{\sigma }={10}^{-1.625}m$ and $m{r}_g=648.6$.