Are black holes more redshifted than the CMB?

[Gerinski]

I don't know if this question makes any sense, sorry if it doesn't.

I have often read that any matter (say an object, for more mundane clarity) falling into a black hole (providing it radiated) would be perceived by an outside observer as never actually crossing the event horizon. It's "image" would become more and more redshifted, to a point where at the event horizon it looks as infinitely redshifted, because there space itself "falls into the black hole" at a rate equal to the speed of light.

Now, the CMBR is also dramatically resdhifted, but not infinitely, only up to 3 K. This kind of suggests to me that a black hole's surface area would appear even more redshifted than the background CMBR which fills up space, it would effectively appear redshifted to 0 K.

Is this reasoning correct? Could we spot black holes by looking at points where the redshifting is even higher than for the CMBR itself? (I can guess that we do not have the technological resolution for that, but just in theory). So that looking at the CMBR in very fine detail, finding "holes" in it which represent points of even lower temperature, zero K precisely instead of 3 K, could help in locating black holes?

Thanks

 

[sevenperforce]

Most black holes are not very large in spatial terms. A black hole with the mass of Earth would be around an inch across; a black hole the size of the Sun would be less than 6 km across. Stellar-mass black holes range from 5-10 solar masses, corresponding to diameters of 30-60 km. A 60-km-wide black hole halfway between Earth and Alpha Centauri (the nearest star to us) would appear to us as a disk 200 times smaller than a penny...if that penny was resting on the surface of the moon.

An easier way to spot black holes is by the way they bend light around themselves, like focusing lenses in space.

 

[mfb]

This kind of suggests to me that a black hole's surface area would appear even more redshifted than the background CMBR which fills up space, it would effectively appear redshifted to 0 K.

Yes.

Could we spot black holes by looking at points where the redshifting is even higher than for the CMBR itself?

No. Black holes are tiny. Actually resolving one in telescopes would need telescopes with a size of the order of ten kilometers (in the visible range). And even then you would still see the matter in front of it - intergalactic matter and the accretion disk around the black hole, which is very hot and does not get redshifted much.

 

[Gerinski]

Thanks guys !

 

[Nixinkome]

I think Gerinski is on to something if only for more sensitive, future measuring systems. What is the distance from the Event Horizon to the 'centre' of a black hole depending on the latter's mass? Nixinkome.

 

[mfb]

Length is not a meaningful quantity to give this "distance". You can give a distance in time - which should be of the order of the Schwarzschild radius divided by the speed of light (plus some numerical prefactor). Microseconds for stellar black holes, seconds to hours for galactic black holes.

 

[Gerinski]

Thanks to all. Just let me remind that my question said "in principle". I acknowledged right away that we currently do not have the required resolution for spotting black holes in this way.

I just said that in principle, finding tiny spots in the CMBR where the temperature seems to be zero, (after the usual re-working of the CMBR image to exclude the effects of any radiating bodies between us and the background image) could lead to determining that in that spot there must lie a black hole in our line of sight.

 

[sevenperforce]

Thanks to all. Just let me remind that my question said "in principle". I acknowledged right away that we currently do not have the required resolution for spotting black holes in this way.

I just said that in principle, finding tiny spots in the CMBR where the temperature seems to be zero, (after the usual re-working of the CMBR image to exclude the effects of any radiating bodies between us and the background image) could lead to determining that in that spot there must lie a black hole in our line of sight.

Gravitational lensing will make the spot hotter than the CMBR, not colder, regardless of the resolution we're using.

 

[Gerinski]

Well, only if gravitational lensing is applicable in that line of sight and distance (of course gravitational lensing is applicable everywhere, I mean whether its observable effects from Earth show anything detectable).

Typical gravitational lensing does not produce a single image covering what really lies in the line of sight, it typically creates things such as Einstein Rings or crosses.

At any rate and if only theoretically, if a black hole lied very close to us, we might spot it by detecting an area of the skies which looked redshifted to zero instead of to the 3K of the CMBR, right? That was the meaning of the question.

Thanks!

 

[mfb]

If the black hole itself does not have material around it and if it does not rotate (or its axis of rotation is aligned with our line of sight), yes. It looks like this then.
If the black hole rotates, or has infalling mass, things get complicated.

 

[Chronos]

The redshift of the EH of a black hole obviously corresponds to 0 Kelvin. Of course you can never measure the redshift of the event horizon of a black hole because it does not emit photons. This, in no way, explains CMB temperature anisotropy.