Black holes' existence from our point of view

[Gerinski]

Hi, layman here,

I have often read that because of time dilation, we would never see any infalling matter actually crossing the event horizon, it would just look more and more redshifted towards becoming invisible, even for infrared or microwave / radio detectors, but never becoming part of the black hole itself, it would seem to stay "frozen" just at the event horizon.

However, I believe it is safe to say that black holes do exist and exert gravitational influence on spacetime and matter around them. Sagitarius A* seems to be a clear example, based on the observed orbits of nearby stars which can only be explained by the presence of the black hole.

So as a layman, I would naively interpret that there seems to be a difference between what we can optically see and what we can gravitationally infer, even if both light and gravity are supposed to propagate at the same speed.

Let's say we have a black hole which 1 million years ago had a mass of 1 million solar masses, and let's take that as our "starting point". We could see it at that time and measure its mass from its gravitational effects.

Since then, matter surrounding it has been pulled in and falling into the black hole, let's say 500,000 solar masses more increasing the black hole's mass to 1.5 million solar masses.

Now, assuming we were able to observe since 1 million years ago, we would not be able to see that those 500,000 solar masses fell into the black hole. From our point of view, they would look just like highly redshifted stuff, approaching the black hole but never actually getting to cross the event horizon and falling into it in order to increase its mass. From our point of view the black hole's mass would still be 1 million solar masses, because the extra 500,000 have not reached it from our point of view, they stay hovering above the event horizon, dramatically redshifted.

But, I guess, the gravitational effects we would observe from the black hole right now would be according to a black hole of 1.5 million solar masses. Right?

If so, how do we reconcile the facts? We see a black hole of only 1 million solar masses exerting a gravitational influence of 1.5 million solar masses (the other 500,000 solar masses do exert gravity but are observed as still hovering above the horizon).

Does this make any sense? Or is it just that the gravitational influence of the 500,000 solar masses, even if we can never see them as becoming part of the black hole, must be computed in order to get the total gravitational influence of the black hole?

TX !

 

[phinds]

Hi, layman here,

I have often read that because of time dilation, we would never see any infalling matter actually crossing the event horizon, it would just look more and more redshifted towards becoming invisible, even for infrared or microwave / radio detectors, but never becoming part of the black hole itself, it would seem to stay "frozen" just at the event horizon.

Yes, in terms of what we can observe that is correct.

However, I believe it is safe to say that black holes do exist and exert gravitational influence on spacetime and matter around them. Sagitarius A* seems to be a clear example, based on the observed orbits of nearby stars which can only be explained by the presence of the black hole.

Correct.

So as a layman, I would naively interpret that there seems to be a difference between what we can optically see and what we can gravitationally infer, even if both light and gravity are supposed to propagate at the same speed.

Correct.

Let's say we have a black hole which 1 million years ago had a mass of 1 million solar masses, and let's take that as our "starting point". We could see it at that time and measure its mass from its gravitational effects.

Since then, matter surrounding it has been pulled in and falling into the black hole, let's say 500,000 solar masses more increasing the black hole's mass to 1.5 million solar masses.

Now, assuming we were able to observe since 1 million years ago, we would not be able to see that those 500,000 solar masses fell into the black hole. From our point of view, they would look just like highly redshifted stuff, approaching the black hole but never actually getting to cross the event horizon and falling into it in order to increase its mass. From our point of view the black hole's mass would still be 1 million solar masses, because the extra 500,000 have not reached it from our point of view, they stay hovering above the event horizon, dramatically redshifted.

But, I guess, the gravitational effects we would observe from the black hole right now would be according to a black hole of 1.5 million solar masses. Right?

Of course. The fact that we can't observe what we know to be happening is irrelevant to its actually happening.

If so, how do we reconcile the facts? We see a black hole of only 1 million solar masses exerting a gravitational influence of 1.5 million solar masses (the other 500,000 solar masses do exert gravity but are observed as still hovering above the horizon).

There is nothing to reconcile. If you are outside the BH, all of the mass that you know to have fallen in is closer to the center of mass than you are and therefore has exactly the same gravitational effect on you as if it actually WERE hovering at the EH.

Does this make any sense? Or is it just that the gravitational influence of the 500,000 solar masses, even if we can never see them as becoming part of the black hole, must be computed in order to get the total gravitational influence of the black hole?

As I said above, the mass is all there and the effects are all there.