Can you fall into a singularity?

[WestAir]

Okay, so I'm not very smart, and lost an argument at work to someone that presumably knows more than me on this subject. Google has given me no help, so I've come here to ask the experts. The argument was:

From the reference frame of an in-falling astronaut, hawking radiation will annihilate him before he has a chance to reach the singularity. From an orbital reference frame: Hawking radiation will cause the black hole to explode before in-falling astronauts pass the event horizon. And so with all possible reference frames, the singularity never interacts with external reference frames. (My co worker also insisted that black holes never form at all, because matter takes longer than the the heat death to collapse)

Is that true? I know you accelerate pretty fast during your plummet but if a black hole is 2 miles across I have a hard time believing you can accelerate to 0.9c, succumb to fantasy-level time dilation, and be nuked by negative energies before your geodesics terminate. I said it wasn't true but I don't know anything about scalars and schwarzchields(sic) and theories.

[cubinator]

1 hour ago, WestAir said:

(My co worker also insisted that black holes never form at all, because matter takes longer than the the heat death to collapse)

Well that's not quite true, we've got a picture of one and it looks pretty black inside. Maybe the singularity is what never forms instead?

The event horizon is the distance at which the escape velocity is c. So, you can reach the event horizon travelling at less than escape velocity, though you'll probably be close to it. I think you'd have to solve some indefinite integrals with relativity equations to calculate which happens first between the collapse of the black hole and your reaching its center. I'm not sure the answer would come intuitively.

[wumpus]

1 hour ago, cubinator said:

Well that's not quite true, we've got a picture of one and it looks pretty black inside. Maybe the singularity is what never forms instead?

The event horizon is the distance at which the escape velocity is c. So, you can reach the event horizon travelling at less than escape velocity, though you'll probably be close to it. I think you'd have to solve some indefinite integrals with relativity equations to calculate which happens first between the collapse of the black hole and your reaching its center. I'm not sure the answer would come intuitively.

And once you cross the event horizon, all physics is undefined.  "Reaching the event horizon" pretty much has to mean "reaching the black hole",  because after that you might as well argue how many angels dance on the head of a pin*.

You need a pretty massive black hole to survive tidal forces just to get to the event horizon (no idea about surviving Hawking radiation.  Presumably your spacesuit has lots of shielding).  Scott Manley (of course) has some interesting videos of what the requirements are to orbit a black hole.

* To answer a related debate, I'd declare that God can indeed create an object so massive he himself can not lift it.  Exhibit A: black holes.

PS: I've been told that using the point where escape velocity = c is cheating and that you're supposed to tensor calculus and general relativity to calculate it, but v_e=c works and is trivial (and I don't know the first thing about tensor calculus).  Although according to Scott Manley, if your Ap is less than twice the radius of the event horizon you are absolutely doomed, and it is only a matter of time before you enter the black hole (no matter how much acceleration your spaceship has).

[StrandedonEarth]

1 hour ago, wumpus said:

to survive tidal forces

Yeah, that's my understanding. You'd get ripped apart by tidal forces before even reaching the event horizon.

[K^2]

1 hour ago, wumpus said:

And once you cross the event horizon, all physics is undefined.

That's not actually correct. It's important to understand that event horizon is a coordinate singularity, not a physical one like the singularity at the center. Event horizon is not a fixed surface, but rather is relative to your frame of reference. Physics is, indeed, undefined if you want to be at rest w.r.t. the singularity, which is impossible once you're bellow Schwarzschild radius, but a free-fall frame exists and is valid. What happens as you fall into a black hole is that the event horizon appears to flatten as you get closer, and then wraps around, creating what's known as Schwarzschild bubble around you. So rather than appearing to be bellow event horizon, which obviously can't work, it appears that absolutely everything in the universe is bellow the event horizon, which surrounds you fully. At no point do you actually experience crossing the event horizon. Also, from perspective of someone falling in, you make it to singularity in finite time. Of course, not in one piece. Even for supermassive black hole, whose "surface" gravity is quite manageable, allowing approach well within Schwarzschild radius, as you get closer to singularity, the tidal effects are still going to reach the point where they pull apart absolutely all matter. So the Schwarzschild radius is still that final judgement point - all trajectories bellow it lead to singularity in finite time.

@WestAir To your original question, I actually don't know. I'm going to pull up some references and might need to crunch some numbers. Intensity of Hawking radiation encountered by a free-falling object should be calculable, but I'm not sure about correct frames of references for the few commonly cited formulas, so I'm going to have to look up a bit more detail on derivation, and hopefully, I'll be able to get back to you quickly with exact numbers.

Edit:

2 minutes ago, StrandedonEarth said:

Yeah, that's my understanding. You'd get ripped apart by tidal forces before even reaching the event horizon.

Depends on the mass of the black hole. The larger it is, the weaker the forces are at the event horizon. Supermassive black holes are actually perfectly fine to approach from perspective of the tidal forces.

Edited June 27, 2020 by K^2

[mikegarrison]

What do you mean by a "singularity", anyway? We know stars that are large enough collapse into black holes. These are too large to "evaporate" by Hawking radiation in any reasonable amount of time. (Extremely small black holes would probably evaporate before they grew.)

The more massive the black hole, the less strong the tidal forces would be. A really massive black hole should have an event horizon big enough that tidal forces wouldn't rip up a person before they fell through it.

As I understand it, an object falling into a black hole appears, from the outside, to slow down in proportion to how close it gets to the event horizon, and so it can never be seen to enter it. But from the point of view of the object itself, the event horizon of a supermassive black hole would basically be more of a non-event horizon. You simply would just head on in.

Edited June 27, 2020 by mikegarrison

[mikegarrison]

4 hours ago, WestAir said:

If a black hole is 2 miles across

I don't think that is a meaningful concept. The event horizon has a radius (Schwarzschild radius). I don't think the black hole itself has a radius. It just has mass.

Edited June 27, 2020 by mikegarrison

[WestAir]

30 minutes ago, K^2 said:

 

@WestAir To your original question, I actually don't know. I'm going to pull up some references and might need to crunch some numbers. Intensity of Hawking radiation encountered by a free-falling object should be calculable, but I'm not sure about correct frames of references for the few commonly cited formulas, so I'm going to have to look up a bit more detail on derivation, and hopefully, I'll be able to get back to you quickly with exact numbers.

 

Having joined the day before me, I always fear that you'll have played enough KSP, gotten bored, and moved on. Yet over the (near-decade) you've never ceased to educate the non-physicists and that's outstanding.

I hope I was right and the math shows that hawking radiation doesn't destroy the singularity before in-falling reference frames reach it in finite time. I reeeeallly want to be right for once lol. Thanks.

14 minutes ago, mikegarrison said:

What do you mean by a "singularity", anyway?

The point where your scalars are infinite.

3 minutes ago, mikegarrison said:

I don't think that is a meaningful concept. The event horizon has a radius (Schwarzschild radius). I don't think the black hole itself has a radius. It just has mass.

I'm a layman and do not use know proper terminology. By "size of black hole" I meant from one end of the event horizon to the other which, I think your correction perfectly describes. I'll use Schwarzschild radius from now on. Thanks Mike!

[Bill Phil]

2 hours ago, mikegarrison said:

I don't think that is a meaningful concept. The event horizon has a radius (Schwarzschild radius). I don't think the black hole itself has a radius. It just has mass.

One can describe a black hole as the region of spacetime encompassed by the event horizon - thus saying "a black hole 2 miles across" works, provided you describe the region as spherical, at least approximately.

Blackholes can have mass, but also angular momentum and charge. The event horizon can also have a temperature.

The singularity of a rotating black hole is sometimes called a ringularity. Which is pretty cool if you ask me.

[Nuke]

17 hours ago, WestAir said:

Having joined the day before me, I always fear that you'll have played enough KSP, gotten bored, and moved on. Yet over the (near-decade) you've never ceased to educate the non-physicists and that's outstanding.

seconded. i might have played ksp maybe a couple days this year, having played it to death in the earlier days. but the forum still has good science content. and its more approachable than an actual science forum somewhere. 

Edited June 27, 2020 by Nuke

[magnemoe]

12 hours ago, StrandedonEarth said:

Yeah, that's my understanding. You'd get ripped apart by tidal forces before even reaching the event horizon.

An stellar black hole yes, however an supermassive one does not have such an strong tide at the even horizon even if much larger simply because the event horizon is much larger. 
You would still have tidal effects inside the event horizon who would screed anything to an string of atoms long before they reached the singularity.

This brings up another weird question. Think all stars rotate and then the resulting black hole should also keep its angular momentum. 
Now as the singularity is just an point this should force the black hole to spin infinite fast but I'm sure its relativistic effects here 

---

Gravity in KSP is in fact an singularity at the center of the planet who is hollow. If you clip trough the terrain you will fall towards it. Interesting you will be shot out of it by ridiculous speed. 
This because the singularity has no collision, also time between calculating in KSP is 0.05 seconds I think. so as you fall the last seconds acceleration start get ridiculous high who also give ridiculous speed and say the last calculation was 50 meter from singularity, the next might be many kilometres away 

[wumpus]

1 hour ago, magnemoe said:

An stellar black hole yes, however an supermassive one does not have such an strong tide at the even horizon even if much larger simply because the event horizon is much larger. 
You would still have tidal effects inside the event horizon who would screed anything to an string of atoms long before they reached the singularity.

This brings up another weird question. Think all stars rotate and then the resulting black hole should also keep its angular momentum. 
Now as the singularity is just an point this should force the black hole to spin infinite fast but I'm sure its relativistic effects here 

---

Gravity in KSP is in fact an singularity at the center of the planet who is hollow. If you clip trough the terrain you will fall towards it. Interesting you will be shot out of it by ridiculous speed. 
This because the singularity has no collision, also time between calculating in KSP is 0.05 seconds I think. so as you fall the last seconds acceleration start get ridiculous high who also give ridiculous speed and say the last calculation was 50 meter from singularity, the next might be many kilometres away 

"Interesting you will be shot out of it by ridiculous speed."  I'd assume that the exit speed depends entirely on the ratio between the distance of the last tick of time before you reached the center vs. the last time after you reach the center.  If the later click was closer, you will presumably slow down and get a second (and possibly third or more) try to have your "final acceleration" higher than the "first decceleration".  Does Kerbol's interior have an atmosphere?

[magnemoe]

6 hours ago, wumpus said:

"Interesting you will be shot out of it by ridiculous speed."  I'd assume that the exit speed depends entirely on the ratio between the distance of the last tick of time before you reached the center vs. the last time after you reach the center.  If the later click was closer, you will presumably slow down and get a second (and possibly third or more) try to have your "final acceleration" higher than the "first decceleration".  Does Kerbol's interior have an atmosphere?

Yes you could get an slow down. however you will get an speed up later who will eject you. 
I don't know how this will work in an atmosphere, only happened on the Mun and Ike for me. 
I expect you to overheat and blow up even on Duna altrough one streamer got an clip trough underwater on Kerbin. 
Problem with the sun or Kerbol or the sun is tat you will overheat long before you reach the surface who I believe had it one kill layer, however one very early KSP version let you pass trough the sun. 
And yes an neutron star would be cool in KSP2 but this get a bit off topic

[kerbiloid]

"When you gaze long into the singularity, the singularity gazes also into you."

[K^2]

13 hours ago, magnemoe said:

This brings up another weird question. Think all stars rotate and then the resulting black hole should also keep its angular momentum. 
Now as the singularity is just an point this should force the black hole to spin infinite fast but I'm sure its relativistic effects here 

Rotating black holes are still a bit of a mystery. We have solutions for everything that happens above the event horizon - it's called Kerr metric, and it has some exciting properties. Like, it allows you to actually go "bellow" event horizon utilizing frame dragging in the ergosphere, which lets you steal a bit of an angular momentum from the black hole to escape from a distance you normally shouldn't be able to.

The singularity of the Kerr metric is a ring that is infinitely thin but has finite radius. Unfortunately, Kerr metric is also known to be unstable in the interior region, which means that the interior of a rotating black hole is not cylindrically symmetric, and that means the singularity is probably not a perfect ring. Without solving for the interior metric, it's impossible to say what it's actually going to be like. If Kerr metric is very close to true solution, it might be as simple as singularity being an ellipse, but there are other possibilities as well.

[kerbiloid]

Spoiler

  

When event horizons intersect.

Spoiler

 

 

[JoeSchmuckatelli]

Okay, I'll be the dumb Jarhead in the room: why are the tidal forces of a Stellar Mass BH more dangerous than those around a Super Massive? 

[K^2]

3 hours ago, JoeSchmuckatelli said:

Okay, I'll be the dumb Jarhead in the room: why are the tidal forces of a Stellar Mass BH more dangerous than those around a Super Massive? 

If you want a precise answer, "because math." But if you are ok with a bit of hand-waving, Schwarzschild radius, which is as close as you'll get to a black hole and have a hope of returning, grows linearly with mass. Tidal forces are an inverse cube relationship with distance from the center and linear with mass. So the larger the black hole is, the lower the tidal forces at Schwarzschild radius. Sure, the black hole is more massive, producing stronger forces overall, but you are also that much further from the center, which is a bigger factor.

[cubinator]

3 hours ago, JoeSchmuckatelli said:

Okay, I'll be the dumb Jarhead in the room: why are the tidal forces of a Stellar Mass BH more dangerous than those around a Super Massive? 

If you imagine space as a sheet bent by gravity (yeah, yeah, I know) then the tidal force is analogous to how steeply the sheet is bent. A supermassive black hole is really huge, like bigger than the whole solar system, so its sheet doesn't bend very quickly over a short distance like the height of a person, or even maybe the size of a planet. But if you look at a stellar-mass black hole, it has essentially the same gravity in the middle (infinite) but it is much smaller, only the size of a city or maybe a large island. So its sheet is practically folded in half, so you'd be torn apart being near there. Imagine laying on a bed that was folded 80 or 90 degrees in the middle, versus laying on a bed that had a slight downward incline. The difference in how comfortable each of those beds are is the difference between a stellar and a supermassive black hole.

[Shpaget]

What confuses me is, if for an outside observer stuff can't fall below event horizon how is it that can we have black holes of different (greater mass? Shouldn't all black holes be equal sizes, just above black hole forming threshold size? Or does matter stop before reaching the event horizon but as more stuff falls inward the EH moves up to encompass the matter that previously approached?

[cubinator]

1 hour ago, Shpaget said:

for an outside observer stuff can't fall below event horizon

No, stuff should be able to fall through the event horizon from our perspective because at that point it's not travelling at quite the speed of light. Only if it got to the singularity would it actually reach the speed of light.

[K^2]

1 hour ago, Shpaget said:

What confuses me is, if for an outside observer stuff can't fall below event horizon how is it that can we have black holes of different (greater mass? Shouldn't all black holes be equal sizes, just above black hole forming threshold size? Or does matter stop before reaching the event horizon but as more stuff falls inward the EH moves up to encompass the matter that previously approached?

This applies to a point mass falling in. Physics of a black hole swallowing something with substantial mass, like a neutron star or another black hole, is different. Black holes merge in finite time producing quite a gravitational splash that we can actually detect with LIGO. And, of course, anything that was close to event horizon when two black holes merge will also get swept up pretty much instantly from our perspective.

That does make a close fly-by of a supermassive black hole both a legitimate way to time-travel forward and an extremely risky one, as it's very easy to get swept up by a gravitational wave of something else falling in.

1 hour ago, cubinator said:

No, stuff should be able to fall through the event horizon from our perspective because at that point it's not travelling at quite the speed of light. Only if it got to the singularity would it actually reach the speed of light.

It's not about light speed. Time dilation at event horizon diverges to infinity. That's part of why event horizon is also called a coordinate singularity, which is different from true singularity at the center. From perspective of observer falling in, you reach Schwarzschild radius in finite time. From perspective of remote observer, it takes infinite time due to that time dilation. But this only works so long as the thing falling in doesn't have enough mass to alter the space-time metric with its own gravity.

[HebaruSan]

I can't tell whether this is fully relevant or not, but in case anyone hasn't seen it, I think this is like a visual representation of some of the stuff K^2 is saying.

Spoiler

 

 

[K^2]

1 hour ago, HebaruSan said:

I can't tell whether this is fully relevant or not, but in case anyone hasn't seen it, I think this is like a visual representation of some of the stuff K^2 is saying.

Yeah, basically. But the instability bit is key. In summary, the moment you get anything inside a Kerr black hole, the interior collapses into something else, and I'm not aware of actual solutions that describe what it becomes. So in real world, the structures described by the video do not actually exist. What does exist may or may not be similar. One strong indication that there are substantial differences is that we haven't found any white holes in our universe. For that reason, anything with an exit to another universe seems unlikely, but a supermassive rotating black hole might still contain a pocket universe under its inner horizon, if, indeed, it has one.

I don't have any high hopes for precise mathematical solutions explaining what's really happening inside a rotating black hole, but it might be possible to find a solution with numerical simulation, but starting with Kerr metric, perturbing it, and simulating collapse to a true ground state. Back when I was in grad school, that seemed entirely out of reach, but there has actually been a lot of progress on simulations with really big data sets in higher dimensions, so we might be getting close to the kind of compute power that this would take. Hopefully, we'll know exactly what sort of things are actually happening inside a rotating black hole soon.

[Bej Kerman]

On 6/27/2020 at 7:35 PM, magnemoe said:

Now as the singularity is just an point this should force the black hole to spin infinite fast but I'm sure its relativistic effects here 

I know it's an old thread, but I just have to bring this up. The singularity does not form a point in a spinning (Kerr) or a spinning and charged (Kerr-Newman) black hole. It turns into a ring, one that still can't spin faster than light. Because space flows outward due to the immense centrifugal forces, but cannot flow back out to the event horizon as space is already falling in at >c, it flows out into new regions of space, forming a wormhole at the middle of the black hole's temporal structure and a white hole that allows exit back into a universe (that resides in the past once you're out and thus cannot be re-entered - approaching a white hole would lead you to the black hole in your future light cone); a spinning black hole could form a bridge between universes. The metric also has a negative radius within the bounds of the ringularity, effectively forming a portal to an anti-verse of negative size.