| Abstract: |
| The latest astrophysical observational data confirm that the universe is expanding with acceleration and that the masses of the black holes are changing over time. This raises the question of the solutions to partial differential equations that model the propagation of waves in a cosmological background with black holes in an expanding universe. We prove the existence of global in time small data solutions of semilinear Klein-Gordon equations in space-time with a black hole with time-dependent mass and static Schwarzschild radius in the expanding universe. We indicate that the damping term of the covariant Klein-Gordon equation is independent of location in the background only if the mass of the black hole is proportional to the scale factor of expansion. This is where the cosmological principle comes into play. |
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