Black hole electromagnetic spectrum

Of course neither a single Schwarzschild nor a single Kerr black hole, nor a pair of these has an emission spectrum, other than the Hawking one. (Nordström and Newman holes must have it while in binaries, but they are not common).
But not having emission spectrum does not rule out having absorption and deflection spectra. Nor of shift spectra.

For light of short wavelength compared to Schwarzschild radius, a single Schwarzschild black hole has simple, black spectrum dictated by geometry. GR can treat light as rays and geometrically derive the amount of light intercepted by event horizon, and deflected by any angle.

But what happens when the wavelength is appreciable compared to the Schwarzschild radius? A black ball would deflect such waves by diffraction. A black hole should have interplay of gravity and diffraction. So what does Schwarzschild black hole cross-section for absorption and deflection do for the parts of spectrum where the wavelength is comparable or bigger than Schwartzschild radius?

Now, I mentioned shift spectra.
A lone Schwarzschild black hole would not shift frequency in a reference frame where it is stationary. Waves would be absorbed or deflected but not change frequency. It would Doppler shift frequency of deflected waves in frames where it moves.
Binary black holes are moving in reference frame where their common centre of mass is stationary, so of course they Doppler shift deflected waves.
But how about Kerr black holes? Is there any frequency shift for electromagnetic waves that pass through ergosphere and get out again?

snorkack said:

But not having emission spectrum does not rule out having absorption and deflection spectra. Nor of shift spectra.

I'm not sure what you mean. An "absorption spectrum" would mean absorbing some wavelengths but not others. A black hole absorbs all wavelengths.

snorkack said:

For light of short wavelength compared to Schwarzschild radius, a single Schwarzschild black hole has simple, black spectrum dictated by geometry.

Where are you getting this from? Do you have a reference?

snorkack said:

Now, I mentioned shift spectra.
A lone Schwarzschild black hole would not shift frequency in a reference frame where it is stationary. Waves would be absorbed or deflected but not change frequency. It would Doppler shift frequency of deflected waves in frames where it moves.

Again, where are you getting this from? Do you have a reference?

PeterDonis said:

I'm not sure what you mean. An "absorption spectrum" would mean absorbing some wavelengths but not others. A black hole absorbs all wavelengths.

Yes, but does the black hole absorb all wavelengths exactly equally?
Even wavelengths that are in the order of magnitude of black hole size?

PeterDonis said:

Where are you getting this from? Do you have a reference?

Reference for what?
For the black hole deflection or absorption of light, a simple example is this:
https://www.spacetimetravel.org/expeditionsl/1
Many references duplicate this simple picture - pure ray geometry.
Which I reworded as "simple black spectrum" - absorption cross-section independent on wavelength.
For the wavelengths where this simple model holds.
What I do not find references for is what happens for wavelengths where this ray optics models necessarily breaks down. A black absorbing obstacle will create a diffraction and interference pattern. Therefore, for a black hole interrogated with a plane wave whose wavelength is appreciable compared to the black hole size, I should expect interplay of gravitational bending with diffraction and interference. Who discuss that?

PeterDonis said:

Again, where are you getting this from? Do you have a reference?

Uh, this?
Basic relativity of light frequency?
If a mirror, in a reference frame where it is stationary leaves the light frequency unaltered then in a reference frame where the mirror moves towards or away from light it Doppler shifts the light - respectively blueshift and redshift.
Therefore, if a Schwartzschild black hole in a reference frame where it is stationary leaves the frequency of deflected light unaltered (it blueshifts when approaching the hole, but redshifts back to exactly the initial frequency when escaping to infinity), in a reference frame where it moves relative to the direction of light direction change it must Doppler shift the light frequency.

snorkack said:

does the black hole absorb all wavelengths exactly equally?

Any light that goes into the hole is absorbed.

snorkack said:

Even wavelengths that are in the order of magnitude of black hole size?

That would depend on which theoretical model you use.

Observationally we can't detect such long wavelengths, so we have no way of checking our theoretical models in this regime.

snorkack said:

Reference for what?

For your claims about the spectrum of a black hole.

snorkack said:

For the black hole deflection or absorption of light, a simple example is this:
https://www.spacetimetravel.org/expeditionsl/1

That's not a valid reference.

snorkack said:

Many references duplicate this simple picture - pure ray geometry.

Then you should have no trouble finding a textbook or peer-reviewed paper.

snorkack said:

What I do not find references for is what happens for wavelengths where this ray optics models necessarily breaks down.

Then you should not be making claims about what happens in that case.

snorkack said:

Uh, this?
Basic relativity of light frequency?

Sorry, no. Either you have a valid reference to back up your claims, or you don't. Since you have said you don't, your claims are personal speculation, which is off limits here.

Thread closed.

snorkack said:

if a Schwartzschild black hole in a reference frame where it is stationary leaves the frequency of deflected light unaltered (it blueshifts when approaching the hole, but redshifts back to exactly the initial frequency when escaping to infinity), in a reference frame where it moves relative to the direction of light direction change it must Doppler shift the light frequency.

As a side note, this has nothing whatever to do with the presence of a black hole; it would be the same in flat spacetime. So it has nothing to do with any claims you are making about black holes.