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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 thispaper, we propose a gravity model where the graviton mass is very small in theusual weak gravity environments, below all the current graviton mass bounds,but becomes much larger in the strong gravity regime such as a black hole'svicinity. For black holes in this model, significant deviations from generalrelativity emerge very close to the black hole horizon and alter the black holequasi-normal modes, which can be extracted from the ringdown waveform of blackhole binary mergers. Also, the enhancement of the graviton mass near thehorizon can result in echoes in the late time ringdown, which can be verifiedin the upcoming gravitational wave observations of higher sensitivity.

Can the graviton have a large mass near black holes?