# 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?

• maybe you should first tell us how you plan to make or catch such a black hole before worrying about kicking it. Dec 2, 2012 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 Dec 2, 2012 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. Dec 2, 2012 at 20:57
• Elias Kiritsis, Mini black-holes at RHIC and LHC, a talk about mini black holes Dec 2, 2012 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 Dec 2, 2012 at 21:03