Radiative falloff in Schwarzschild-Einstein-de Sitter spacetime
The evolution of a scalar field in Schwarzschild-Einstein-de Sitter spacetime is studied numerically. The spacetime has two distinct regions: an inner black hole region and an outer cosmological region. Early on in the evolution the field behaves as if it were in pure Schwarzschild spacetime, with each multipole of the field first exhibiting quasi-normal ringing followed by a power-law decay. However, later in the evolution the field learns of the existence of the cosmological region and changes behaviour. For the 'l' = 0 mode, the field first changes behaviour when it reaches the discontinuous potential at the boundary. The field then decays again with a power-law falloff, but with a slower decay rate than in the pure Schwarzschild case. For the ' l' > 0 modes of the field, the field again first changes behaviour when it reaches the discontinuous potential at the boundary, but this time the change in behaviour is characterized by a Doppler-shifted echo of its earlier quasi-normal oscillations.