Black Hole impact Q's

So this is a spin-off from the "How could we see an approaching black
hole" thread...

Small black holes could exist, say the theorists.

Let's consider a really small black hole - say, 100kg in mass. This
would have a very, very, very small event horizon. Were it to impact
the earth, dead-on, at the same sort of speed that we would expect
asteroidal or cometary impacts, what would happen?

Would there be any resistance to its passage?

Woud it come to rest or bore straight though?

If the former, would it eventually absorb the entire earth, and if so,
how long would "eventually" be?

If it went straight through, how big a hole would there be in the
earth on exit?

wrote:
So this is a spin-off from the "How could we see an approaching black
hole" thread...

Small black holes could exist, say the theorists.

Let's consider a really small black hole - say, 100kg in mass. This
would have a very, very, very small event horizon. Were it to impact
the earth, dead-on, at the same sort of speed that we would expect
asteroidal or cometary impacts, what would happen?

100kg black hole is smaller than quarks - the earth looks like a vacuum
to it.
On the other hand, it would undergo Hawkins evaporation in short order
and become a 100kg 100% mass conversion bomb - should be a pretty good
bang. (However, any such will have already popped.)

First of all the stellar black holes are at lest a min of 3 solar weights,
that means it's going to be bigenough that the earth would be just a little
someing as it passed threw the system. Being that we're fall less than even
one solar weight, we'd be just a slight munch and the earth would be
distroyed as it crossed the hevent horzen. Like a fly hitten the windsheld
of an 80mph 18 wheeler.


--
There are those who believe that life here, began out there, far across the
universe, with tribes of humans, who may have been the forefathers of the
Egyptians, or the Toltecs, or the Mayans. Some believe that they may yet be
brothers of man, who even now fight to survive, somewhere beyond the
heavens.


The Lone Sidewalk Astronomer of Rosamond
Telescope Buyers FAQ
http://home.inreach.com/starlord
Sidewalk Astronomy
www.sidewalkastronomy.info
The Church of Eternity
http://home.inreach.com/starlord/church/Eternity.html


wrote in message
...
So this is a spin-off from the "How could we see an approaching black
hole" thread...

Small black holes could exist, say the theorists.

Let's consider a really small black hole - say, 100kg in mass. This
would have a very, very, very small event horizon. Were it to impact
the earth, dead-on, at the same sort of speed that we would expect
asteroidal or cometary impacts, what would happen?

Would there be any resistance to its passage?

Woud it come to rest or bore straight though?

If the former, would it eventually absorb the entire earth, and if so,
how long would "eventually" be?

If it went straight through, how big a hole would there be in the
earth on exit?

On Tue, 13 Feb 2007 16:07:52 GMT, wrote:

So this is a spin-off from the "How could we see an approaching black
hole" thread...

Small black holes could exist, say the theorists.

Let's consider a really small black hole - say, 100kg in mass. This
would have a very, very, very small event horizon. Were it to impact
the earth, dead-on, at the same sort of speed that we would expect
asteroidal or cometary impacts, what would happen?

Would there be any resistance to its passage?

Woud it come to rest or bore straight though?

If the former, would it eventually absorb the entire earth, and if so,
how long would "eventually" be?

If it went straight through, how big a hole would there be in the
earth on exit?

First, you need to decide what "small" means. If you mean this is a
primordial black hole (and that there is no Hawking radiation to
evaporate it), then it will pass through the Earth if it approaches at
greater than Earth's escape velocity, and end up orbiting inside the
Earth if it approaches slower. Such a black hole has a very tiny cross
section (sub-atomic), so it ought to be able to orbit inside the Earth
for a very long time with little interaction. (This scenario has been
studied as part of some risk analysis work conducted at Brookhaven,
where it was suggested such a black hole might be created artificially.)

However, if by small you mean millimeters, I'm sure the effect of a
collision would be quite devastating- like a large meteor, and the tidal
and tectonic effects of such an object orbiting inside the Earth would
be unpleasant. I'm not sure how long it would take a black hole that
size to consume the Earth- months or years?

There have been several good science fiction stories based on this idea-
Greg Bear, Larry Niven, and others.

_________________________________________________

Chris L Peterson
Cloudbait Observatory
http://www.cloudbait.com

On Feb 13, 4:22 pm, lal_truckee wrote:
wrote:
So this is a spin-off from the "How could we see an approaching black
hole" thread...

Small black holes could exist, say the theorists.

Let's consider a really small black hole - say, 100kg in mass. This
would have a very, very, very small event horizon. Were it to impact
the earth, dead-on, at the same sort of speed that we would expect
asteroidal or cometary impacts, what would happen?

100kg black hole is smaller than quarks - the earth looks like a vacuum
to it.

A rough estimate of its diameter at 100kg would be ~ 10^-24 m.
And its time to live would be of the order of Tevap ~ 4 x 10^-12 (4
ps)
This seems far too short a lifetime to be useful.

If we restrict the game to consider a primeval BH that is well on its
way to expiring but still has a million years left to live (chosen to
make the numbers easy). Then it would have a mass of about 10^-20 of a
solar mass or roughly 10^10 kg (ignoring small factors).

And the diameter of a 10^10 kg BH would be around 10^-16m and still
much smaller than an atom (~10^-9m). So to first order this tiny black
hole will barely notice us because there is so much empty space
between the atoms. It will not be inconvenienced much beyond a minor
gravitational perturbation.

The rock within a cylinder a few millimetres? from the trajectory will
notice an abrupt transient gravitational force from it and also the
energy released by any matter it does encounter. A ballpark estimate
of its capture cross section would be 10^-30m^2 along a 10000km track
which would be 10^-23 m^3 or about 10^-19 kg (being generous). Yield
mc^2 ~ 0.01 J from swallowing matter. However, the shockwaves from
elastic deformation of the Earths crust in the second or so it took to
transit hypersonically through the Earth might well cause some trouble
- particularly near the exit wound.

A BH with a diameter about the same as an atom and weighing 10^16kg
would make for a much more complex scenario. Its capture cross section
and energy released then being something like 10^12 times larger =
0.01TJ or 10T TNT equivalent which still is surprisingly small. I
expect the shockwave then would become a serious problem.

I suspect a distant observer with a high speed camera would observe
something reminscent of the amour penetrating round going through an
apple only with a larger ratio between the entrance and exit wounds.

Note that the BH collision on the face of it would be preferable to an
encounter with an asteroid of equal mass!

Numbers subject to revision for typos and arithemetic error.

(This question has previously been discussed on sci.physics.relativity
a few years back - there wasn't much of a consensus)

On the other hand, it would undergo Hawkins evaporation in short order
and become a 100kg 100% mass conversion bomb - should be a pretty good
bang. (However, any such will have already popped.)

Yes. Making a 100kg BH would be a very unwise experiment.

Regards,
Martin Brown

On 2007-02-13, Martin Brown wrote:
[...considering a small black hole traversing the earth...]
And the diameter of a 10^10 kg BH would be around 10^-16m and still
much smaller than an atom (~10^-9m). So to first order this tiny black
hole will barely notice us because there is so much empty space
between the atoms. It will not be inconvenienced much beyond a minor
gravitational perturbation.

The rock within a cylinder a few millimetres? from the trajectory will
notice an abrupt transient gravitational force from it and also the
energy released by any matter it does encounter. A ballpark estimate
of its capture cross section would be 10^-30m^2 along a 10000km track
which would be 10^-23 m^3 or about 10^-19 kg (being generous). Yield
mc^2 ~ 0.01 J from swallowing matter. However, the shockwaves from
elastic deformation of the Earths crust in the second or so it took to
transit hypersonically through the Earth might well cause some trouble
- particularly near the exit wound.

Hmm, that's interesting -- could you explain why? Given that it'd
be travelling supersonically, how would the effect on the Earth at
its exit point be different from near the entrance point?

Also, traversing the Earth in a second or so is pretty speedy --
say 10000 km/sec. If I had to guess how fast a primordial black hole
would be moving relative to us, I'd have supposed something like
our galaxy's speed relative to the microwave background, or our sun's
orbital speed within the Milky Way, both a few hundred km/sec.
Sorry if this is being nitpicky -- but I'm wondering if you are considering
some effect I hadn't thought about...

Stuart Levy

On Feb 17, 5:31 am, Stuart Levy wrote:
On 2007-02-13, Martin Brown wrote:
[...considering a small black hole traversing the earth...]

And the diameter of a 10^10 kg BH would be around 10^-16m and still
much smaller than an atom (~10^-9m). So to first order this tiny black
hole will barely notice us because there is so much empty space
between the atoms. It will not be inconvenienced much beyond a minor
gravitational perturbation.

The rock within a cylinder a few millimetres? from the trajectory will
notice an abrupt transient gravitational force from it and also the
energy released by any matter it does encounter. A ballpark estimate
of its capture cross section would be 10^-30m^2 along a 10000km track
which would be 10^-23 m^3 or about 10^-19 kg (being generous). Yield
mc^2 ~ 0.01 J from swallowing matter. However, the shockwaves from
elastic deformation of the Earths crust in the second or so it took to
transit hypersonically through the Earth might well cause some trouble
- particularly near the exit wound.

Hmm, that's interesting -- could you explain why? Given that it'd
be travelling supersonically, how would the effect on the Earth at
its exit point be different from near the entrance point?

Essentially most projectile impacts share this characteristic to some
extent. On the way in the penetrating round hits a solid object
leaving a V shaped shockwave in its wake. This does comparatively
little or no damage as the shocked material is supported from behind.
But on the way out there is some back pressure and stored elastic
energy in the wake of the projectile and when the conical shockwaves
hit the surface they are pushing it upwards and outwards but there is
nothing behind to support it from spalling off. The back pressure then
has a means to escape and pushes a plug of material out.

Same sort of thing if you drill a hole (or shoot through) wood that is
not supported from behind. The entrance side is a relatively clean
hole, but the exit is messy with splinters.

Also, traversing the Earth in a second or so is pretty speedy --
say 10000 km/sec. If I had to guess how fast a primordial black hole
would be moving relative to us, I'd have supposed something like
our galaxy's speed relative to the microwave background, or our sun's
orbital speed within the Milky Way, both a few hundred km/sec.

My mental arithmetic error. I had meant to use 100000m/s (100km/s), It
could probably be anything between 30km/s and 500km/s but perhaps with
no upper limit depending on how it came to be a low mass wandering
BH.

Sorry if this is being nitpicky -- but I'm wondering if you are considering
some effect I hadn't thought about...

No a simple arithemetic error.

Interestingly I notice that the HEP groups have actually considered
the potential risks of making ultra low mass BHs in the newest
supercolliders and proved that they would never swallow enough mass to
be self sustaining before undergoing spontaneous evaporation by
Hawking radiation. Some of the current theoretical models allow for
the possibility of some strange shaped BH configurations at the ultra
micro scale of fundamental particles and smaller.

Regards,
Martin Brown