micro black hole forces

A black hole would radiate mass optimally for interstellar-travel applications in the range between $10^7$ and $10^8$ kilograms. Assuming a light-only radiation emission spectrum, with a parabolic reflector with efficiency $f$, this would create an acceleration

$$a = \frac{f P}{mc}$$

$$a = \frac{ f \hbar c^5 }{ 15360 \pi G^2 M^3}$$

$$a = \frac{ f 10^{24} m \times sec^{-2}}{M^3}$$

The problem is that the schwarzschild radius at this mass is a few attometers, which creates a host of problems:

1) the rate at which it can feed from normal matter is too small compared to the rate BH mass is being radiated

2) any electric charge we throw in the BH will be quickly radiated by super radiance effects and Schwinger pair production, so it will stay neutral most of the time.

3) only super hard gamma rays have (to my limited knowledge) the short enough wavelength in order to scatter against such a tiny BH

By the 3 points above, it is unclear how to apply a back-force on the black hole so that a payload, comprising at least of the parabolic reflector, can be accelerated with it

are there any ideas out there about how to exert a force or moment on such a tiny black hole?

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maybe you should first tell us how you plan to make or catch such a black hole before worrying about kicking it. – anna v Dec 2 '12 at 20:21
a rough idea is presented here: arxiv.org/abs/0908.1803 which i wrote a question about a few days ago: physics.stackexchange.com/q/45189/955 – lurscher Dec 2 '12 at 20:28
The attometer dimensions are 10^-3 smaller then the dimensions of a proton. At these dimensions quantum mechanics reigns, so all these classical calculations cannot hold, imo. A quantum theory of gravity is necessary and it does not exist. Some string phenomenologists have put forward mini black holes as a side result of large dimensions in some of the compactified dimensions in string theory, and the masses that come out are nowhere near the values you quote. – anna v Dec 2 '12 at 20:57
Elias Kiritsis, Mini black-holes at RHIC and LHC, a talk about mini black holes – anna v Dec 2 '12 at 20:59
yes, however, large dimensions haven't been observed (yet) at LHC, while the above should apply in the semi-classical regime. If there are no large dimensions, then the usualy planck energy/radius will be bigger/smaller and hence this analysis should apply – lurscher Dec 2 '12 at 21:03

Gravity is the only force remaining to use for capture and co-acceleration. It turns out that there's a reasonable sweet spot in the design space. Mutual attraction between BH and ship balances the thrust on the ship via reflection of the radiation off the paraboloid, which is attached to the ship. A ship-BH separation measured in centimetres up to a good fraction of a metre is achievable in some cases, but this must be dynamically adapted to the m(t) evaporation of the BH. When the BH lies aft of the focus, the system self-corrects to some extent. Trouble brews when the BH wanders off focus to the ship side - then the ship has to devise a way to add temporary extra acceleration via auxiliary engines. This whole arrangement is a nontrivial control problem, of course.

I don't have a handle on how fast an attometer-scale radius BH loses its charge as a fraction of its lifetime. If this charge evaporation time is long enough, we can hope to send an electron beam in to keep the charge topped up. I have not seen any attempts at this calculation. Were that to be possible, BH capture and control becomes far more tractable.

With a single BH of ~1 Mtonne, we can send a manned ship to Alpha Centauri in about 19.5 years of ship time, including decelerating to a stop - a highly asymmetric operation for these BHs. But these past few days I have been playing with "staged" BHs, and, for two BHs of masses ~0.9 and ~0.4 Mt, this ship time (including braking to a stop, again) comes down to about 12.5 years. It is therefore to be expected that extrapolation of this BH staging technique using N BHs, so as to maintain about 1 gee throughout the trip, will be able to get us to the nearest star, and stop, within 3.5 years ship time, which is the theoretical minimum at a constant 1 gee.

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A 1 Mton BH is quasi-bulimic, as you've noted. Therefore, "stick it to a magnet" (or indeed to a charged body) is likely to be the best solution. – Andrew Palfreyman Dec 28 '14 at 14:11
yes, definitely this is the way to go for this. Of course, you could probably not risk using this inside a planetary surface (unless you were really good at the dynamically self-correction of the gravitational anchor). – lurscher Jun 25 '15 at 18:24