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The decreasing of the inertial mass density, established in the past for
dissipative fluids, is found to be produced by the inertial'' term of the transport equation. Once the transport equation is coupled to the dynamical equation one finds that the contribution of the inertial term diminishes the effective inertial mass and the gravitational’’ force term, by the same
factor. An intuitive picture, and prospective applications of this result to
astrophysical scenarios are discussed.

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