Yet another black hole™ physics question

[lyssword]

OK, I have searched this forum, but it seems the topic didn't come up yet.

Anyways I was wondering what the physics of detonating nuclear weapon close to black hole would be? If you detonate a nuke at event horizon for example, would we see the flash? What if it's a mini- black hole (man-made perhaps?), not star-swallowing one, would it veer off course , or be destroyed?.

 

[wuliheron]

Its a nonsensical question along the lines of can God create a rock so big even he can't lift it. If you shot a nuclear weapon towards a sizable black hole it would first be stretched miles long and by the time it got near the event horizon it would be torn apart into pure energy and fundamental particles. No boom. Assuming you could somehow magically teleport it intact close to the event horizon it would still be torn apart into little pieces long before any chain reaction could occur.

As for a mini black hole, it just depends how big it is and how close it gets to the missile.

 

[Biftheunderstudy]

Actually, you could get one close to supermassive black hole no problem. The tidal forces scale inversely as the mass.

That said, its still pretty non-sensical. Read up on what an outside observer sees as an object approaches an event horizon and that should help answer your question.

 

[wuliheron]

Actually, you could get one close to supermassive black hole no problem. The tidal forces scale inversely as the mass.

That said, its still pretty non-sensical. Read up on what an outside observer sees as an object approaches an event horizon and that should help answer your question.

That's assuming the supermassive black hole isn't surrounded by an accretion disk that wouldn't vaporize the missile. No one has ever observed such a black hole and its even debatable whether one could exist even as the universe approaches heat death. Either way its the same result, the tidal effects or some other gravitational effect make it impossible to get near the event horizon of a large black hole intact.

 

[Sunny129]

That's assuming the supermassive black hole isn't surrounded by an accretion disk that wouldn't vaporize the missile. No one has ever observed such a black hole and its even debatable whether one could exist even as the universe approaches heat death. Either way its the same result, the tidal effects or some other gravitational effect make it impossible to get near the event horizon of a large black hole intact.

yes - it is debatable whether one could exist in and around such conditions, but only in the sense that we have yet to prove that we can exist in such conditions. fortunately there is some hope, as not all black holes have accretion disks, and the ones that do don't have them all the time.

but the results are not the same when comparing an object approaching the EH of a stellar mass BH and and object approaching the EH of a supermassive BH. the radius of a supermassive BH (the distance from the singularity to the EH, if you can call it that) is much larger than that of a stellar mass BH. so an object can fall through the EH of a supermassive BH long before it ever encounters tidal forces strong enough to stretch it to smithereens.

 

[JackSpadesSI]

Did you just trademark the term "black hole"?? I hope that was a typo.

 

[SagaLore]

First, do you understand the physics of a nuclear bomb?

 

[PlasmaBomb]

yes - it is debatable whether one could exist in and around such conditions, but only in the sense that we have yet to prove that we can exist in such conditions. fortunately there is some hope, as not all black holes have accretion disks, and the ones that do don't have them all the time.

but the results are not the same when comparing an object approaching the EH of a stellar mass BH and and object approaching the EH of a supermassive BH. the radius of a supermassive BH (the distance from the singularity to the EH, if you can call it that) is much larger than that of a stellar mass BH. So an object can fall through the EH of a supermassive BH long before it ever encounters tidal forces strong enough to stretch it to smithereens.

For someone that knows what the event horizion is, you should know that's incorrect.

Take 2 black holes, one with a Schwarzschild radius of 10 km (approximate for a stellar black hole) , and one with a Schwarzschild radius of 1000000 km (supermassive).

The equation for gravitational field strength is -

So at the event horizion of the Stellar black hole the gravitational acceleration is -

(g/10000m) x (10000m/c)^2 = 0.5

0.0001g x (1.11 x 10^-9) = 0.5

g = 4493775893684 m/s

So at the event horizion of the supermassive black hole the gravitational acceleration is -

(g/1000000000m) x (1000000000m/c)^2 = 0.5

0.000000001g x (0.111) = 0.5

g = 4493775893.684 m/s


(Though these results seem strange... I was expecting the gravitational forces at both points to be ~3x10^8 (or slightly higher)... whereas both are significantly larger (10^9 and 10^12))

 

[Sunny129]

For someone that knows what the event horizion is, you should know that's incorrect.

Take 2 black holes, one with a Schwarzschild radius of 10 km (approximate for a stellar black hole) , and one with a Schwarzschild radius of 1000000 km (supermassive).

The equation for gravitational field strength is -

So at the event horizion of the Stellar black hole the gravitational acceleration is -

(g/10000m) x (10000m/c)^2 = 0.5

0.0001g x (1.11 x 10^-9) = 0.5

g = 4493775893684 m/s

So at the event horizion of the supermassive black hole the gravitational acceleration is -

(g/1000000000m) x (1000000000m/c)^2 = 0.5

0.000000001g x (0.111) = 0.5

g = 4493775893.684 m/s


(Though these results seem strange... I was expecting the gravitational forces at both points to be ~3x10^8 (or slightly higher)... whereas both are significantly larger (10^9 and 10^12))

for someone who seems to know a thing or two about BH physics, you should know that i am correct. i never said that the sheer acceleration wouldn't be enough to instantaneously kill someone (just like the extreme acceleration, or more appropriately deceleration, of a car going 100mph and hitting a concrete wall is enough to kill someone). but if you re-read my statement, you'll see that at no point was i talking about sheer acceleration - i was talking about tidal forces. and if you think about it, a tidal force isn't really force at all - its the difference in gravitational forces at different distances from a gravitating body.

unlike a stellar mass BH (whose radius is orders of magnitude smaller than that of a supermassive BH), the radius of a supermassive BH is so large that the difference in gravitational forces over short distances, for instance between a location just outside the EH and a location just inside the EH, is negligible. i.e. the tidal forces of a supermassive BH are negligible near its EH b/c it is so far from the singularity at its center. so again, while the sheer acceleration at the EH (which is an insane number, as you showed us with your calculation) would instantaneously kill someone, the tidal forces at that same location would not...in fact, they'd hardly be noticeable.

 

[Corrode]

According to this, biggest black hole has a mass equivalent to 18 billion solar masses.

Therefore, its Mass will be ~ 35.8 x 10^39 kg
And Radius will be ~ 5.36 x 10^13 m
And Gravitational Acceleration @ EH will be ~ 830 metres per second^2

Which is 83g. Not much I would say, as far as machines are concerned.

Here @ EH, Escape velocity = velocity of light

A person whose mass is 80kg here will be 6640kg @ EH

From Wikipedia, the Sprint thermonuclear missile accelerated at 100 g, reaching a speed of mach 10 in 5 seconds.

Or am I missing something??

 

[aaronkaufman]

old post, but still:

unless i'm mistaken, sheer forces matter only to a rotating black hole, and there are proportional to the angular momentum and the radius [event horizon] from the COM [singularity]. (in fact, that's the whole idea behind the existence of the ergosphere in a kerr BH, i believe.)

and now getting to the point: while you're right that an infalling observer to a sufficiently supermassive black hole would not be effected by the tidal forces until long after passing the EH [long being relative, i know it's just a few seconds until the tidal forces become significant, and excuse the pun], and that SBH's would be expected to rotate so quickly that the infalling observer would be sheered out of existence at most points of the EH, consider:

what about the two poles where the axis of rotation crosses the event horizon (and also at the same two points the ergosphere)?

wouldn't, at those two special points, both the sheer effects from the rotation AND the spaghettification due to the tidal "forces" be negligable, allowing an infalling observer to survive passing through the EH?

i mean, he'd die shortly after from the spaghettification and/or sheering (if his infalling motion was *ANY* bit deviant from purely linear. [i haven't done the calculation, but i'd imagine the width of his body would be enough that his right and left arms would be subjected to crushing and opposite linear accelerations in opposing directions shortly after he fell in]. but still, wouldn't he be able to observe his dissent for a few seconds?

-A

 

[Sunny129]

old post, but still:

unless i'm mistaken, sheer forces matter only to a rotating black hole, and there are proportional to the angular momentum and the radius [event horizon] from the COM [singularity]. (in fact, that's the whole idea behind the existence of the ergosphere in a kerr BH, i believe.)

and now getting to the point: while you're right that an infalling observer to a sufficiently supermassive black hole would not be effected by the tidal forces until long after passing the EH [long being relative, i know it's just a few seconds until the tidal forces become significant, and excuse the pun], and that SBH's would be expected to rotate so quickly that the infalling observer would be sheered out of existence at most points of the EH, consider:

what about the two poles where the axis of rotation crosses the event horizon (and also at the same two points the ergosphere)?

wouldn't, at those two special points, both the sheer effects from the rotation AND the spaghettification due to the tidal "forces" be negligable, allowing an infalling observer to survive passing through the EH?

i mean, he'd die shortly after from the spaghettification and/or sheering (if his infalling motion was *ANY* bit deviant from purely linear. [i haven't done the calculation, but i'd imagine the width of his body would be enough that his right and left arms would be subjected to crushing and opposite linear accelerations in opposing directions shortly after he fell in]. but still, wouldn't he be able to observe his dissent for a few seconds?

-A

i'm assuming you are responding to me since i'm the only one who's talked about "sheer" anything prior to you in this thread. let me just clear things up a bit here...i was talking about acceleration at the time, not forces. and i used the word "sheer" to indicate that i was talking about the BH's acceleration ONLY (at the EH), independent of any tidal forces which may be present (and which may or may not be substantial at the EH, depending on the mass of the BH). as for "shear" forces, that's a completely different animal, and is not typically associated with BH's (see wiki)...and so i'm not sure it is meaningful to say that someone or something could be sheered out of existence at the EH. perhaps what you're thinking of is frame dragging, in which spacetime within the [relatively] immediate vicinity of a rotating BH gets dragged along with it as it rotates. but i don't know that that would kill anyone, and i would tend to think that one would just get dragged along unharmed with spacetime itself, unless the angular or radial accelerations (caused by immense gravity) were large enough at the EH.

that said, only a spatially one-dimensional object (something with length, but no width or depth, such as a line) could pass through either of the 2 points where the boundary of the ergoshpere and the poles of the EH of a Kerr BH...and that's just from a theoretical point of view. in reality nothing is truly one-dimensional - anything and everything of substance in our universe exists in 3 spatial dimensions. and in reality, you could never test this b/c nothing can ever cross the EH of a Kerr BH at either of those points. a BH's mass and rotation is such that it causes any incoming object that doesn't have enough momentum to escape its gravitational pull to fall int orbit around it until it eventually spirals in. its been shown that an object held stationary with respect to a gravitating body at a distance of "infinity" (or a very large distance for our purposes) and dropped/released such that its initial trajectory is perfectly radial to the gravitating body will not actually smash into the gravitating body on a direct course for its center of gravity - rather it will veer off that radial course as it approaches and will fall into orbit around the gravitating body.

so even if a BH is large enough that tidal forces won't kill you as you cross the EH, and even if frame dragging won't kill you at that point either, you could never survive the acceleration caused by the BH's gravity at the EH...and even if you could somehow survive that acceleration, the universe is such that it is physically impossible to cross at the points where the poles of the EH meets the boundary of the ergosphere due to the inevitability that you would first fall into orbit around the BH before crossing the EH and falling in. its the frame dragging that ensures that you eventually cross the EH near its equator, and nowhere near its poles.