Flash-fried Spaghettification

[modest]

I read something that Craig wrote in another thread...

 

While it’s true that star-mass black holes have such sever radiation and tidal effects near their event horizons that nothing made or ordinary matter could survive there, for hypothetical gigantic ones like the supermassive black holes which appear to be at the center of every Milky Way-like galaxy, this isn’t necessarily true. Solving the tidal force equation

[math]F=\left( \frac1{r_0^2} - \frac1{(r_0+L)^2} \right) G M m[/math]

for a body length [math]L= 2 \,\mbox{m}[/math] with mass [math]M= 50 \,\mbox{kg}[/math], representing a human body at distance [math]r_0[/math] from a large mass [math]M[/math], we find a human-comfortable tidal force of about 1140 N (about the same as hanging by your arms from a tree limb) at the event horizon of a [math]6 \times 10^{34} \,\mbox{kg}[/math] (about 3 million solar masses) black hole.

 

So, if you could handle the environmental nastiness – mostly lots of dangerous radiation – and the space travel problem of getting there, you could fairly easily stop time by traveling to near our galaxy’s central supermassive black hole.

 

[my bold]

 

and I would ordinarily agree with this completely. As far as the radiation goes, I assume Craig is referring to:

 

As matter spirals into a black hole, the intense gravitational gradient gives rise to intense frictional heating; the accretion disc of a black hole is hot enough to emit X-rays just outside of the event horizon. The large luminosity of quasars is believed to be a result of gas being accreted by supermassive black holes. This process can convert about 10 percent of the mass of an object into energy as compared to around 0.5 percent for nuclear fusion processes.

http://en.wikipedia.org/wiki/Accretion_disc

 

But, when I read Craig's post it got me thinking along lines that I have never heard expressed before. My train of thought has led me to the conclusion that no ordinary matter could cross any event horizon intact no matter the weakness of the tidal force nor the state of (or, even, the absence of) the accretion disc.

 

My thinking is that gravitational time dilation as well as gravitational redshift/blueshift are reciprocal; which is to say, if a clock below me in a gravitational well runs slow by some factor and its light, emitted toward me, is redshifted by some factor due to gravitational potential, then that clock will recon the exact opposite as regards to me. My clock will run fast by that same factor and my light will be blueshifted by that same factor from its perspective. GPS clocks are a straightforward example. They run fast from our perspective via gravitational time dilation and our clocks run slow from their perspective (by the same factor) via gravitational time dilation.

 

So... trying to keep this short...

 

Imagine an observer sitting just outside an event horizon of some black hole. From our perspective, at a distance much further from the hole, the observer's clock is near-infinitely dilated toward the slow side. Its light is near-infinitely redshifted. The observer's time has nearly stopped and redshifted to the point of making it practically impossible to observe.

 

On the reciprocal side, the observer falling in the hole nearly reaching the event horizon must expect our clocks out here in the rest of the universe to run nearly-infinitely fast. Our light, directed the observer's way, is likewise near-infinitely blueshifted from that observer's perspective.

 

In a practical sense, this makes the environment near the event horizon of a black hole (any black hole) completely unsurvivable to any matter. As the observer falls closer and closer to the horizon the sky would be brighter and brighter (the intensity would increase) as all of the starlight from any particular star falling on this observer would arrive in very short order. The same would be true of the CMB.

 

Likewise, the starlight and the CMB which is arriving at an enormous rate is being blueshifted into shorter and shorter wavelength gamma rays.

 

By the time the observer has nearly reached the event horizon the environment would be filled with an unsurvivable amount of extremely-high intensity gamma rays. It would be vaporized, and worse. Molecular bonds would be broken. Atoms would be photodisintegrated. As a result, any matter trying to cross any event horizon would be converted to energy before it could reach that horizon.

 

If the above is true then there should be observational consequences of this. A significant portion of the radiation resulting from this matter-energy conversion should be radiated away from the black hole. Most naively, we should expect black holes to glow, or radiate, a rather-steady energy from the process.

 

It may be possible to predict aspects of the spectrum of black holes based on these assumptions.

 

Before we get that far, have I gone wrong somewhere? Is it possible for macroscopic chunks of matter to cross an event horizon?

 

~modest

[Don Blazys]

Quoting Modest:

A significant portion of the radiation resulting from this matter-energy conversion should be

radiated away from the black hole. Most naively, we should expect black holes to glow,

or radiate, a rather-steady energy from the process.

 

If such radiation could be observed, then how would we distinguish it from "Hawking radiation"?

 

Don.

[modest]

Quoting Modest:

 

 

If such radiation could be observed, then how would we distinguish it from "Hawking radiation"?

 

Don.

 

It would be non-thermal (hawking radiation is thermal while a black hole's typical radio emissions which we observe are not) and it would, hopefully, be a bit brighter.

 

Before saying for sure, we would need to calculate at what distance from a typical black hole atoms like hydrogen and helium are converted to photons, and at what exact wavelength exactly we would see that light. We could compare that to, for example, the spectrum of the black holes Sag A or M31* at the center of the Milky way and Andromeda galaxy. I haven't yet calculated, but I wonder if this might be tentatively a better explanation than I have seen thus far—which, has always seemed somewhat lacking and ad hoc.

 

~modest

[Don Blazys]

Quoting Modest

I haven't yet calculated, but I wonder if this might be tentatively

a better explanation than I have seen thus far—

which, has always seemed somewhat lacking and ad hoc.

 

Mathematical plausibility is plausibility.

 

I say, try working out the equations, and if they do work out,

then just toss your idea out there and see if it flies. :)

 

All of these models and theories have now evolved into

"explanations" that are much stranger than fiction anyway!

 

Don.

[Qfwfq]

My clock will run fast by that same factor and my light will be blueshifted by that same factor from its perspective.

No doubt. That's the trouble with people using phrases like "time slows down" without getting across the actual meaning of these things. To each, time is what it is to them.

[CraigD]

I nominate this thread for best title to date in 2011! :) :thumbs_up

 

As more physicists than I can number have written in science for amateur books, physics tends to gets weird to the point of absurdity when calculations give zeros and infinities, as in the case with gravitational blueshift and time dilation at the event horizon (Schwarzschild radius) of a black hole.

 

The only salvations from the infinitely blueshifted/infinite energy radiation modest describes I can imagine are:

• Make sure your black hole is someplace really, really dark
  If the gigantic black hole we’re talking about is an entire universe (if you calculate the Schwartzchild radius of the visible universe using best estimates of its mass, it comes tantalizing close to the best estimates of its radius, suggesting that the entire universe is a black hole), surrounded by nothing, not even CMBR.
   
  The physics of it are over my head, but SF has at least one description (specifically, in Greg Egan’s 2002 novel Schild's Ladder) of experiments conducted in super dark/cold environments created by giant, artificial shades/shields in order to isolate them from external radiation. Perhaps such a scheme would work for approaching a black hole, as I guess you need only be concerned with infalling radiation, as any outfalling will be gravitationally redshifted to finite energies.
   
  
• Get lucky/quantum weirdness
  Our blueshift discussion is treating light as a wave, but as a particle, it may be that the probability of an actual interaction with a photon or other particle blueshifted to infinite or very high energy is zero or close to it, when calculated in exact detail (the doing of which is again over my head). So maybe a body crossing an event horizon with low tidal force wouldn’t get zapped, or zapped severely enough to fail.
   
  
• Don’t go to the event horizon, have it come to you
  I’m not sure this makes any sense, but if the black hole in question is gaining mass, its Schwarzschild radius increasing perhaps the physics are different than approaching one that’s unchanging or decreasing.
  

That’s it for my list of how it might be possible to cross an event horizon without being flash-fried. Now, a couple of my own ideas of why it might be impossible:

• Black holes evaporate
  At the event horizon, for an arbitrarily small duration by the traveler’s clock, an infinite amount of time passes on a distant observers clock. Assuming the theory’s right, however, we know that even supermassive black holes will eventually evaporate due to Due to Hawking radiation. So, an infinitesimal instant after the traveler reaches the event horizon, its black hole will have evaporated, and there will be no more event horizon to reach.
   
  Upon further though reflection, this doesn’t strike me as reason why crossing an event horizon is impossible, but rather that doing so is a one-way trip to the very far, future, after the supermassive black hole in question has evaporated. For an about galaxy-size black hole, the evaporation time is about [math]10^{100}\,\mbox{years}[/math], a hypothetical (other theoretical possibilities exist) far future era known by cosmologists as the Dark Era.
  
• The body crossing the event horizon has non-zero length
  Speaking roughly, as my toes reach the event horizon, but my ankles and above are still above it, an infinite amount of time passes for my ankles and above. So, to an observer in my toes, everything above that has long dies and decayed to dust before it joins it.
   
  This sounds very weird, and at least as un-survivable as spaghettification!
  

[modest]

I say, try working out the equations, and if they do work out,

then just toss your idea out there and see if it flies. :)

 

It sounds fun, I will. I hope I'm up to the task. The more I think about it, the more I realize I'm unfamiliar with the physics. We'd have to consider how the sky changes shape near an event horizon. It would take some doing.

 

~modest

[modest]

No doubt. That's the trouble with people using phrases like "time slows down" without getting across the actual meaning of these things. To each, time is what it is to them.

 

Yeah, I think that should be stressed Otherwise, it helps perpetuate a common misconception.

 

~modest

[modest]

I nominate this thread for best title to date in 2011! :) :thumbs_up

 

:hihi:

 

The only salvations from the infinitely blueshifted/infinite energy radiation modest describes I can imagine are...

 

•Make sure your black hole is someplace really, really dark

 

Yeah, I see no reason why that wouldn't be at least a theoretical solution.

 

•Get lucky/quantum weirdness

Our blueshift discussion is treating light as a wave, but as a particle, it may be that the probability of an actual interaction with a photon or other particle blueshifted to infinite or very high energy is zero or close to it, when calculated in exact detail (the doing of which is again over my head). So maybe a body crossing an event horizon with low tidal force wouldn’t get zapped, or zapped severely enough to fail.

 

I could not discount that.

 

•Don’t go to the event horizon, have it come to you

I’m not sure this makes any sense, but if the black hole in question is gaining mass, its Schwarzschild radius increasing perhaps the physics are different than approaching one that’s unchanging or decreasing.

 

I actually considered that. I think either way you'd be faced with the possibly unfavorable environment just outside the event horizon.

 

...Now, a couple of my own ideas of why it might be impossible:

•Black holes evaporate

At the event horizon, for an arbitrarily small duration by the traveler’s clock, an infinite amount of time passes on a distant observers clock. Assuming the theory’s right, however, we know that even supermassive black holes will eventually evaporate due to Due to Hawking radiation. So, an infinitesimal instant after the traveler reaches the event horizon, its black hole will have evaporated, and there will be no more event horizon to reach.

 

Upon further though reflection, this doesn’t strike me as reason why crossing an event horizon is impossible, but rather that doing so is a one-way trip to the very far, future, after the supermassive black hole in question has evaporated. For an about galaxy-size black hole, the evaporation time is about [math]10^{100}\,\mbox{years}[/math], a hypothetical (other theoretical possibilities exist) far future era known by cosmologists as the Dark Era.

 

My first thought is that hawking radiation is caused exactly at the event horizon. It is not until an observer is below the horizon that the observer recons its clock runs fast. I don't think it would spit out an observer as much as it might hang above the observers head somewhere as the observer falls either to the forming singularity (if one has not yet formed) or to the previously-formed singularity.

 

 

•The body crossing the event horizon has non-zero length

Speaking roughly, as my toes reach the event horizon, but my ankles and above are still above it, an infinite amount of time passes for my ankles and above. So, to an observer in my toes, everything above that has long dies and decayed to dust before it joins it.

 

Yeah, I think the Schwarzschild metric is somewhat lacking in this case because it is static. The Schwarzschild metric says that over any distance between a point set outside the Schwarzschild radius and a point on the Schwarzschild radius, time dilation will be infinite over that distance (even if the distance is as small as a meter-sized man). This is true but it carries with it an unreal assumption—it mostly reflects the fact that the Schwarzschild metric assumes that all points are stationary.

 

From the perspective of the person's head, if it were staying stationary one meter above the horizon, the person's feet would be infinitely redshifted and time dilated if those feet were staying stationary on the horizon. Via the equivalence principle, it is the same as saying that the person is accelerating with infinite acceleration. Replacing the human with an accelerating elevator which is a more-recognizable symbol of the equivalence principle, the rate of a clock at the top of the accelerating elevator is [math]e^{ah/c^2}[/math] times the rate at the bottom. As acceleration goes to infinity, time dilation goes infinite.

 

Light emitted from the bottom of the elevator (or, at the person's feet standing on the event horizon) would never reach the elevator's top (or the person's head staying stationary a meter above the horizon). But, infinite acceleration is required in either case so we know it isn't possible. If the person were freefalling into the horizon, I think the metric would turn out quite a bit different. I think the time dilation between the feet and head of the freefalling observer would be no greater than the tidal force between the head and feet would suggest. If the tidal force were small then just by conservation of energy, the redshift between the two would have to be small. Remember that the photon emitted from the person's feet is being observed at the head at a position closer to the center of the black hole than when it was emitted. Both the person and the light are falling into the hole. The person is just falling a bit quicker.

 

I guess that description was probably far longer than it needed to be. Sorry :)

 

But,

 

This sounds very weird, and at least as un-survivable as spaghettification!

 

The weirder the better. I love thinking about this stuff

 

~modest

[Qfwfq]

The weirder the better. I love thinking about this stuff

Trouble is, these things are so full of pitfalls; even when using the proper covariant equations there are pitfalls in interpreting what one gets, so it's not easy to get things straight.

[modest]

Trouble is, these things are so full of pitfalls; even when using the proper covariant equations there are pitfalls in interpreting what one gets, so it's not easy to get things straight.

 

I don't think I could overstate my agreement.

 

Do you know of any metric or method of solution that would solve the relative time dilation between one clock stationary relative to a spherically symmetric mass and another that is freefalling relative to the mass? My initial premise was that time dilation and redshift were reciprocal, but I wonder if above the weak field limit they are not in the case where one observer is static and another is not ('static' I should say... static relative to Schwartzchild coordinates).

 

~modest