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If a supernova created an outward-going electromagnetic wave with an extremely large amplitude and wavelength and this wave eventually reached a smaller black hole what would happen?

Assuming the amplitude and wavelength are both larger than the Schwarzschild Radius.

Would the wave be able to travel through the black hole by "tunneling"?

What I mean by that is if the probability of the the position of the wave-particle was mostly outside the Event Horizon it might pass through.

Or would space-time geometry affect the wave before it reached the Event Horizon so the wave was altered enough that it would be captured?

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    $\begingroup$ What do you mean by an amplitude larger than the Schwarzschild Radius ? $\endgroup$
    – TimRias
    Feb 12, 2020 at 23:29
  • $\begingroup$ @mmeent - Imagine someone creating a wave along a rope by arm movement. A maximal arm movement creates a peak in the rope's movement. From the rope's static position to this peak is the wave amplitude. If I have a black hole I can define the Schwarzschild Radius as the "distance" from r=0 to the event horizon. If I have a small black hole I could possibly create a wave amplitude in a rope which is bigger than the Schwarzschild Radius. Astrophysically I imagine there would need to be an event like a supernova to create such a large wave. Is there something wrong since you ask? $\endgroup$
    – BlackHoleSlice
    Feb 13, 2020 at 14:21

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For a Schwarzschild black hole, some of the wave’s energy gets scattered in various directions by the hole, and some gets absorbed, increasing the mass of the hole. For low frequency / large wavelengths, the hole has little effect on the wave; most of the energy of a plane wave continues propagating in the original direction. For high frequency / small wavelengths, absorption becomes dominant. When the wavelength is comparable to the Schwarzschild radius, scattering in various directions is significant.

The relevant (and somewhat miraculous) equation for studying this kind of physics mathematically is called the Teukolsky equation. It actually applies to fields of various spins propagating in the spacetime of a Kerr black hole. Electromagnetic fields around Schwarzschild holes are just one case to which it applies.

The mathematics is simplest for a scalar (spin 0) field and a Schwarzschild hole. This paper is an approachable introduction to this physics. Rather than dealing with the more complicated Teukolsky equation, it shows how the Klein-Gordon equation for a scalar field in a Schwarzschild spacetime reduces to a radial Schrodinger-like equation with a simple effective potential which makes the reflection (scattering) vs. transmission (absorption) somewhat intuitive.

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