B Theories about light and time near a black hole

[GR86]

TL;DR Summary

Discussing the physics of the bending of space/light, near a black hole, in laymens terms.

First off, i don't know if this has been discussed by other people openly, it was just something i have wondered for a long time.

OK. The event horizon marks the distance, spherically, where anything moving at the speed of light (including light), has it's escape velocity overcome. So closer than the event horizon and not even light has the velocity to overcome the curvature of space. And further than the event horizon and light can escape. Simple so far. But what about that EXACT distance of the event horizon, i picture this sphere as a satellite path for light. Does this make sense?

So, light from whatever source, will move towards a particular black hole. Much of it will be angled so as to be "sucked in" and never leave. Much of it will just pass by, just outside the event horizon and continue it's journey. But a small portion will hit the sweet spot and end up orbiting a black hole. At least this is what makes sense. But as more and more light accumulates, im picturing a sphere of unimaginable density of light, forever orbiting a black hole but never to be seen by anybody since we only detect light when it hits our eye or a sensor.

Now i said forever but this isn't really true (correct me if im wrong). First, if a black hole absorbs enough matter, won't it's added mass change the distance of the event horizon? If so, then the theorized light sphere will only be present until that happens. Second, is there any equation that tells us how much time dilation there is, relative to 1g on earth, at an event horizon? By our perspective, the light would redshift to basically standing still as it approached a black hole (if we could actually see it), so how much time is really passing at an event horizon relative to earth? Is 1 second at an event horizon equal to a billion years our time? Is this something we know yet?

That last question brings me to theory #2. This one is a bit out there but still interesting. What if black holes are explosions happening in slow motion? Is there anybody out there promoting an idea like this, where each black hole could be the beginning of a big bang? If time dilation is so immense as to virtually stop time in relation to our 1g on earth, how can we possibly know what's really happening within it? I tend to understand things visually so im just thinking out loud. It's like when science talks of the age of the universe, that concept seems wrong from the start as the universe is nothing more than pockets of differing density of matter, and therefore differing fields of spacetime curvature. All of matter is not the same "age" since time dilation creates an uneven passage of time. Relatively speaking of course.

Any thoughts welcome, i have thought about some of this for decades and decided to find somewhere to ask it.

 

[Nugatory]

OK. The event horizon marks the distance, spherically, where anything moving at the speed of light (including light), has its escape velocity overcome. So closer than the event horizon and not even light has the velocity to overcome the curvature of space. And further than the event horizon and light can escape.

That’s not right. The event horizon is not related to escape velocity the way you’re thinking (you can escape from a gravity well even at speeds less than escape velocity, just not on a ballistic trajectory, but you can’t escape from a black hole on any trajectory) and the “distance” you’re thinking of is not a meaningful concept (the center of a black hole is not a point in space so can’t have a distance to anywhere). Escape velocity at a radius from the center is not a good starting point for reasoning about black holes.

is there any equation that tells us how much time dilation there is, relative to 1g on earth, at an event horizon? By our perspective, the light would redshift to basically standing still as it approached a black hole (if we could actually see it), so how much time is really passing at an event horizon relative to earth? Is 1 second at an event horizon equal to a billion years our time? Is this something we know yet?

”Time really passing” at the event horizon is another unhelpful concept. Time passes at the same rate, one second per second, everywhere.
When we talk of time dilation we mean something like the following: I’m watching a remote clock, I calculate (allowing for light travel time) that at the same time that my clock reads $T_0$ the remote clock reads $T_{0’}$, a moment later at the same time that my clock read $T_1$ the remote clock reads $T_{1’}$, $T_{1’}-T_{0’}\lt T_1-T_0$, we have to time dilation (and the result has nothing to do with “time really passing” at the remote location and everything to do with how we’ve defined “at the same time”).
But there’s no way of doing this with an event horizon. First, the entire procedure requires that the remote clock stay at the same place for two consecutive readings, and it’s not possible to be stationary at the event horizon; and second there is no non-arbitrary way of defining “at the same time” here.

That last question brings me to theory #2.

To speculate effectively about black holes, you have to start with an accurate mental model of what they are. Other posters will be able to suggest some good sources

 

[Ibix]

i picture this sphere as a satellite path for light. Does this make sense?

That would be the photon sphere, which is not the same as the event horizon. For a non-rotating black hole, the photon sphere lies at 1.5 times the event horizon radius.

But as more and more light accumulates,

It doesn't. All orbits of the sort you are imagining are unstable - the slightest perturbation and into the hole it goes. Perturbations such as the passing of another light pulse would be enough. So the black hole grows.

That last question brings me to theory #2

As @Nugatory points out, your mental model of a black hole seems wildly wrong. And frankly, you need to understand the maths to correct it. Scientists use mathematical models because they work, not just for fun.

If you want to learn the maths, you probably need to start with special relativity, and you may find you need to review non-relativistic mechanics once you do. I rather like Taylor and Wheeler's Spacetime Physics, which can be downloaded for free from Taylor's website or bought on paper. Others prefer Morin's Relativity for the Enthusiastic Beginner, the first chapter of which is free to read online. Once you understand SR, you can start on GR. I used Carroll's online lecture notes, but you may find other sources suit you better. The minimum maths for GR is orders of magnitude harder than SR.

If you don't want to study maths, a former mentor here named Ben Crowell teaches a course called Relativity for Poets, the text for which is free to download from his www.lightandmatter.com. It's honest about the limitations of such an approach, I think.

It's like when science talks of the age of the universe, that concept seems wrong from the start as the universe is nothing more than pockets of differing density of matter, and therefore differing fields of spacetime curvature. All of matter is not the same "age" since time dilation creates an uneven passage of time.

The figure quoted for the age of the universe is the time measured by co-moving observers. Most observers aren't co-moving, correct, but for anybody who hasn't spent the entire hostory of the universe orbitting tightly round a black hole the difference is way less than our measurement uncertainty on that figure.

 

[Dale]

i picture this sphere as a satellite path for light. Does this make sense?

The satellite path for light is called the photon sphere. It is further out than the Schwarzschild radius.

But as more and more light accumulates, im picturing a sphere of unimaginable density of light, forever orbiting a black hole but never to be seen by anybody since we only detect light when it hits our eye or a sensor.

You are correct about not seeing this light if you are not actually at the photon sphere. But light won’t progressively accumulate. The orbit of light at the photon sphere is unstable. So light will leave, especially light that was emitted elsewhere.

 

[GR86]

The satellite path for light is called the photon sphere. It is further out than the Schwarzschild radius.

You are correct about not seeing this light if you are not actually at the photon sphere. But light won’t progressively accumulate. The orbit of light at the photon sphere is unstable. So light will leave, especially light that was emitted elsewhere.

Ok i had never heard of the photon sphere but that's what i was describing. It would be more interesting if it were stable but i had a hunch it wasnt as any mass changes affect the gravity of the black hole.

 

[Nugatory]

but that's what i was describing.

Were you? You were describing stuff happening at the event horizon, while the photon sphere is well outside of the horizon.

 

[Nugatory]

Ok i had never heard of the photon sphere but that's what i was describing. It would be more interesting if it were stable but i had a hunch it wasnt as any mass changes affect the gravity of the black hole.

Is that really what you were describing? You were asking about stuff that happens at the event horizon. The photon sphere lies well outside the event horizon. The instability of the orbits has nothing to do with mass changes, indeed the calculations showing orbital instabilitly are done under the assumption of fixed mass.

 

[GR86]

Were you? You were describing stuff happening at the event horizon, while the photon sphere is well outside of the horizon.

I was describing the accumulation of photons, orbiting a black hole in a spherical manner, can you think of another phenomenon similar that i might have been describing? Was i just shooting darts and making stuff up and got lucky? No, i just happened to be wrong about the distance of the balancing point. I think you are being pedantic and hung up on being EXACTLY right when i was trying to convey an idea to see if it had validity. It does and i know what to call it now.

 

[GR86]

That’s not right. The event horizon is not related to escape velocity the way you’re thinking (you can escape from a gravity well even at speeds less than escape velocity, just not on a ballistic trajectory, but you can’t escape from a black hole on any trajectory) and the “distance” you’re thinking of is not a meaningful concept (the center of a black hole is not a point in space so can’t have a distance to anywhere). Escape velocity at a radius from the center is not a good starting point for reasoning about black holes.
”Time really passing” at the event horizon is another unhelpful concept. Time passes at the same rate, one second per second, everywhere.
When we talk of time dilation we mean something like the following: I’m watching a remote clock, I calculate (allowing for light travel time) that at the same time that my clock reads $T_0$ the remote clock reads $T_{0’}$, a moment later at the same time that my clock read $T_1$ the remote clock reads $T_{1’}$, $T_{1’}-T_{0’}\lt T_1-T_0$, we have to time dilation (and the result has nothing to do with “time really passing” at the remote location and everything to do with how we’ve defined “at the same time”).
But there’s no way of doing this with an event horizon. First, the entire procedure requires that the remote clock stay at the same place for two consecutive readings, and it’s not possible to be stationary at the event horizon; and second there is no non-arbitrary way of defining “at the same time” here.To speculate effectively about black holes, you have to start with an accurate mental model of what they are. Other posters will be able to suggest some good sources

I disagree, there is a non arbitrary way of defining "at the same time", it's called now. It doesn't matter the level of time dilation between two differing perspectives, now is now for both. And of course locally time passes at 1 second per second, but why would i mean that when discussing time dilation? I think this is just a game of semantics. If i describe time "passing" at different rates when discussing differing time dilation, it should go without saying im speaking in relative terms.

 

[jbriggs444]

I disagree, there is a non arbitrary way of defining "at the same time", it's called now. [...]

You sorely need a course in special relativity. This is all wrong.

Start with this.

 

[PeterDonis]

what about that EXACT distance of the event horizon, i picture this sphere as a satellite path for light. Does this make sense?

No. The photon sphere, where light makes a circular orbit around the black hole, is outside the event horizon, at a radial coordinate that is 3/2 of the horizon's radial coordinate.

The light that is "stuck" at the event horizon, staying there forever, is moving radially outward.

if a black hole absorbs enough matter, won't it's added mass change the distance of the event horizon?

It will increase the surface area of the horizon. There is no meaningful concept of "distance of the event horizon", because the black hole does not have a "center" in the sense you are thinking, the sense in which an ordinary spherical object does. The locus $r = 0$ is not a place in space; it's a moment of time (which is to your future if you're anywhere inside the horizon).

is there any equation that tells us how much time dilation there is, relative to 1g on earth, at an event horizon?

I don't know what you mean by "relative to 1 g on earth". However, it is impossible for any observer to "hover" at the event horizon, even for an instant, so the question of how much "time dilation" there is at the horizon relative to anything is meaningless. The concept simply doesn't make sense at or inside the horizon.

That last question brings me to theory #2.

This is personal speculation and is off limits here.

 

[PeterDonis]

I think this is just a game of semantics.

No, it's not. What it is, is you having some common misconceptions about black holes, that you will need to correct. I have tried to correct at least some of them in my post #11.

 

[GR86]

It will increase the surface area of the horizon. There is no meaningful concept of "distance of the event horizon", because the black hole does not have a "center" in the sense you are thinking, the sense in which an ordinary spherical object does. The locus $r = 0$ is not a place in space; it's a moment of time (which is to your future if you're anywhere inside the horizon).

Im not sure why the word center keeps being used, i never mentioned center. A black hole isn't a hole as you know, in theory it is still a body of mass, likely symmetrically round. I assumed any meaningful distance measured like an event horizon, would be measured from the assumed "surface" of the black hole, not from a center point. This is all theoretical anyhow, nobody is measuring anything from within a black hole.

I don't know what you mean by "relative to 1 g on earth". However, it is impossible for any observer to "hover" at the event horizon, even for an instant, so the question of how much "time dilation" there is at the horizon relative to anything is meaningless. The concept simply doesn't make sense at or inside the horizon.

The twin paradox is impossible for us to test as we can't send a twin at near speed of light, yet we still discuss it. Discussing how much time is distorted near a black hole, relative to that on earth, is still useful if it helps educate people on the mechanics of physics.

 

[PeroK]

The twin paradox is impossible for us to test as we can't send a twin at near speed of light, yet we still discuss it.

The twin paradox is only a distraction for laymen and popular science authors. Physicists are interested in the relativistic energy-momentum relations, which are tested in every high-energy particle experiment.

This is 2025, not 1905. You have 120 years of physics to learn if you want to say anything important.

 

[Ibix]

The twin paradox is impossible for us to test

Hafele and Keating would like a word.

 

[GR86]

You must be one of the "experts" peter mentioned. You keeping posting personal insults so i guess you get a warning too? LOL What a joke, gotta love academia nowadays, filled with intellectuals who can't handle anybody challenging them.

 

[PeroK]

You must be one of the "experts" peter mentioned. You keeping posting personal insults so i guess you get a warning too? LOL What a joke, gotta love academia nowadays, filled with intellectuals who can't handle anybody challenging them.

Far from it. I'm just an amateur student. But I do know this stuff up to a certain level and know how much I don't know.

A reality check is not an insult.

Physics is hard work. It always was.

 

[Ibix]

You keeping posting personal insults

Do I? My last is slightly sarcastic, sure, but hardly insulting. What else have I posted that's insulting?

intellectuals who can't handle anybody challenging them.

I left academia decades ago, and I didn't specialise in relativity when I was there. Apart from two eight hour courses as an undergrad, everything I know about relativity has come from self-study.

You aren't challenging anything. You're simply making wrong statements (ones that we've seen before, because they're common misunderstandings of relativity) and not appearing to try to learn anything from us when we try to point out where you're wrong.

 

[PeterDonis]

Im not sure why the word center keeps being used, i never mentioned center. A black hole isn't a hole as you know, in theory it is still a body of mass, likely symmetrically round. I assumed any meaningful distance measured like an event horizon, would be measured from the assumed "surface" of the black hole, not from a center point.

This is all wrong. A black hole has no surface. It's not a body of mass. It's vacuum. Just vacuum that has enough spacetime curvature to have an event horizon.

This is all theoretical anyhow, nobody is measuring anything from within a black hole.

If you're not willing to accept the predictions of our best current theory of spacetime, General Relativity, then this thread is pointless because we have no theory to use to make predictions.

The twin paradox is impossible for us to test as we can't send a twin at near speed of light, yet we still discuss it.

Yes, because we can use our best current theory of spacetime to make predictions about it. The same way we make predictions about black holes.

Discussing how much time is distorted near a black hole, relative to that on earth, is still useful if it helps educate people on the mechanics of physics.

But it's not if it misleads people, which is what the concept of "time distortion" appears to be doing for you.

 

[PeterDonis]

You must be one of the "experts" peter mentioned. You keeping posting personal insults so i guess you get a warning too? LOL What a joke, gotta love academia nowadays, filled with intellectuals who can't handle anybody challenging them.

This thread is now closed, and you are going to receive a warning for this post. This attitude is not productive and will not be tolerated here.

 

[Nugatory]

The twin paradox is impossible for us to test as we can't send a twin at near speed of light, yet we still discuss it.

It has been tested. Google for the Hafele/Keating experiment, which directly measured the effect using clocks accurate enough that we didn’t need relativistic velocities to produce a measurable effect.