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At first I assumed the amplification factor meant an increase in brightness. But since the equation: $$A(u)=\frac{u^2+2}{u\sqrt{u^2+4}}$$ is independent of mass, this make no sense to me. Wouldn't everything be infinity magnified (if its mass independent empty space should work, right)? Even if its simply not valid for a zero mass, everything would be amplified by an arbitrarily high amount any time even a neutrino passes arbitrarily close to the right $u$? But if its not brightness, I don't know what signal is being amplified.

mjgreen
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Gravitational lensing is just geometry, as is optical lensing. The amplification factor describes the increase of the area of the image (at constant surface brightness).

BTW, the amplification factor does depend on the mass $M$ of the lens, since $u=\theta/\theta_E$ and $\theta_E$ depends on $M$. Here $\theta$ and $\theta_E$ are the relative angular distance between source and lens and the radius (angle) of the Einstein ring for the lens, respectively.

Walter
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  • I think it is the second part here that answers the question. You could explain what theta and theta_E represent. A picture of the geometry would be even better. – James K Mar 03 '17 at 23:32