# Gravitational time dilation and event horizons question

## Main Question or Discussion Point

I want to ask a question about science/physics. To me and my level of education, this has not been answered, though I am sure there is someone out there that can provide the answer.

It regards something I have been pondering due to gravitational time dilation (and space dilation I suppose, if that is the right term). Particularly I am led to consider the idea that, the speed of light remaining constant, there is a red shift if the light is observed from a further distance from the mass.

I understand that some of the mathematics pertaining to gravitational time dilation relate the relative time of an event observed locally to a time measured at an infinite distance from a mass. My issue is more to do with the relative warping of spacetime.

Consider a black hole. The current maths – I believe – based on the above reference frames says that at the event horizon of a black hole time stops, and therefore that within the black hole the rules of physics do not hold due to imaginary numbers/roots of negative numbers, etc. However, I am trying to consider the issue from various positions relative to the event horizon. Let’s use vertical height to describe distance from the centre of mass.

The axioms forming my query are this:

1. if the same beam of light shone towards a mass increases in frequency (and decreases in wavelength) it is effectively shrinking. Or alternatively, since the same object occupies different relative space, the space within which it exists is larger.

2. If the speed of light is constant to the observer, how could it possibly be that anything could prevent its escape? I understand the current maths might support the collapse of physical laws as we know them inside an event horizon (as well as providing a mathematical location at which the event horizon exists), but I propose that as an axiom it is worth considering what makes sense – in this case, is it not more likely that the light is still travelling away from the black hole at the same speed but that the frequency has been reduced to such a degree that it is not observable? Ie, time does not “stop” rather space there is so large that from the outside you would be searching for 1 photon per millennia, or some other such equivalent.

On the basis of those axioms, I would consider the case for an observer some great distance away, and for a second observer who to the first appears to be just outside the event horizon. My rationalisation would be that if I was the second observer – that much closer to the source of mass – my relative time and space is distorted to the extent that I can see further into the black hole than the first observer. My relative time is that much slower that I am able to detect the 1 photon per millennia as – say – 1 photon per minute. All of a sudden, the event horizon is no longer similarly situated. It appears to be a good distance towards the black hole. What difference does the relative observation of someone an infinite distance from the mass make to me?

Let’s take this a step further. Put a third observer inside the first observers event horizon. Again, this observer may still see an event horizon ahead somewhere, but they do not see themselves inside it. On this basis, does the relative event horizon shrink dependent upon how close you are to the black hole. In the end, doesn’t this continued expansion of relative space provide the possibility to allow for the fact that mass has to occupy the same space to form a singularity? It seems to me that the black hole is not making mass occupy the same space, but rather the space is relatively larger, you just need to be close to be able to comprehend or see it.

My view – which I am more than prepared to accept is incorrect – is that perhaps the maths we have supports what we are able to observe, but to someone with sufficient capability and understanding this thought may enable someone to improve our understanding of physics further. I suggest it is more likely others have pursued this logic and that I am wrong – but what if they haven’t?

As I say, I know that the maths may not support my axioms, but if the principle of axioms is that they are used as the basis of a theory to contend with the current maths/theory in place then I think they warrant consideration. Sadly, my understanding is not deep enough, and my maths skills not strong enough, to take my thoughts further.

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PeterDonis
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Hi wolverwookie, and welcome to PF!

The current maths – I believe – based on the above reference frames says that at the event horizon of a black hole time stops
No, that's not what our current theory (General Relativity, and specifically the Schwarzschild solution to the Einstein Field Equation) says. It says that the event horizon is an outgoing lightlike surface. The view that "time stops" for a light ray is not correct, though it often appears in pop science discussions.

and therefore that within the black hole the rules of physics do not hold due to imaginary numbers/roots of negative numbers
No, this is not correct at all. GR and the Schwarzschild solution cover the event horizon and the region inside it perfectly well.

if the same beam of light shone towards a mass increases in frequency (and decreases in wavelength) it is effectively shrinking.
No, it isn't. A light ray does not "occupy space" the way you are thinking it does.

If the speed of light is constant to the observer, how could it possibly be that anything could prevent its escape?
Because the measurement of the speed of light by an observer is local--you can only directly measure the speed of light that is passing you--but the concept of "escape" is global. Local measurements of a light ray can't tell you what will happen to it long after it passes you; that depends on global properties of the spacetime. In a black hole spacetime, the global properties are such that outgoing light rays at the event horizon stay at the event horizon, so they don't escape.

I won't comment on the rest of your post since the "axioms" you are basing your speculations on are incorrect.

Hi Peter, thank you for the response, that gives me some more things to look into (and sorry for the incorrect use of axioms, I was just trying to be clear over the rationalisations I was making). As I said, I know I am short on the detail of these things but its something I have had going through my mind. I will investigate the points you have made!