Light travelling towards a black hole

jamesbolt
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I think I am wrong in what I am about to say so I someone could explain relatively simply where I went wrong I would be thankful...

When light travels towards a black hole it's wavelength increases it's frequency and decreases it's wavelength due to the increase in energy. Because a black hole is infinitely dense when light gets close enough the energy provided by the infinite density (ie infinite energy) would mean the wavelengths would get infinitely close...

If this is true then theoretically there should be a boundary of electromagnet energy that cannot get closer because the wavelength is infinitely close...
Is this true? Or have I missed something?
 
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jamesbolt said:
Because a black hole is infinitely dense...

You are confusing the central singularity with the event horizon.
 
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