Black Hole impact Q's

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