Light absorbed by black holes why?

Question

Why is light absorbed by black holes while it is massless as theory of gravitation works only for masses?

Answer 1

Newton's theory of gravity only prescribes a force between massive objects. However, neither photons nor black holes are correctly treated by Newton's theory. Instead, you need Einstein's theory of gravity: General Relativity. That theory simply says that a massive object — in this case, the black hole — literally changes the geometry of space and time around it. The photon simply follows a "straight line" (a geodesic) through this spacetime. It turns out that this path appears curved, and can curve straight into the black hole itself, depending on the photon's trajectory.

The energy of the photon doesn't play a particularly strong role in determining this geodesic as long as it's very small compared to the mass-energy of the black hole. (Otherwise, the photon's own energy would also change the geometry in complicated ways.) In this sense, Einstein's theory is more one-sided than Newton's — but only for massless objects. Even in Newton's theory, if one object $m$ is far less massive than the other $M$, you can pretend the smaller one is moving while the larger one remains fixed (as we might for a ball thrown in the gravitational field of the Earth). Then, the smaller mass cancels out from the equation of motion: \begin{equation} F = m\, a = G_\mathrm{N} M\, m / r^2 \qquad \mathrm{or} \qquad a = G_\mathrm{N} M / r^2. \end{equation} That is, the acceleration is independent of the mass of the smaller object, and just depends on the mass of the larger object. Of course, you learned that in elementary physics. Strictly speaking, Newton's theory doesn't tell us what happens to a truly massless object, but we might imagine extending it to that case by just assuming the same acceleration.