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The late-time dynamics of massive spin-2 fields in flat and curved spacetimes are studied analytically. We find that the time evolutions of the massive fields are characterized by oscillatory power-law decaying tails at asymptotically late times. In a flat spacetime the decaying exponent depends on the multipole number and the parity of the mode. In the curved Schwarzschild black-hole spacetime the decaying exponent is found to be universal.

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