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mfb

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In terms of the total light you get, the smaller size wins.Samshorn said:Right, but the question is, which of those effects wins?

We cannot get a black disk, but we can get a disk that is so small that you don't see it any more, even with the increased brightness per area.

Some more mathematics: If I consider the ultra-relativistic limit here,

$$n(\omega,\Omega)d\omega d\Omega \approx \frac{\omega T_{eff}}{2\pi^2}d\omega d\Omega$$ and

$$T_{eff} \approx 2T_* \gamma$$

Therefore, the brightness increases with the relativistic gamma-factor, while the area scales with ##\gamma^{-2}## (?). This would give a total luminosity (in the visible range) which scales with ##\gamma^{-1}## for very high speeds.