# Black hole with NO radiation

I've been recently thinking about black holes and...,

...let's say we have a black hole that doesn't radiate anything. Then you will drop this black hole to some solid surface (let's say the black hole has relatively small mass -> $0{,}5$ $\mathrm{kg}$, which implicates very big density and let's also say that this surface is Earth surface). We know that anything below Schwarzschild radius ($R_s=2G_EM_d/c^2$) cannot escape from the black hole. And here's my question: How can I compute how many of surrounding matter can black hole swallow in some given amount of time (for example 3 hours or 2 days)? Or how long does it take for the black hole to swallow $2$ $\mathrm{kg}$ of matter.

Thanks a lot!

Edit: In reaction to the first comment...I would abandon any geothermal and thermodynamical processes. You're currently at Earth's surface and black hole you just made, you recently dropped. Gravitional field is heading towards the geometric center of Earth and that is where the hole is heading (free fall?). Earth has almost none density compared to our black hole, so that black hole will fly threw it like nothing, yet cannot leave Earth because of gravity. That way it will be oscillating. I want just a model of how this could be computed (amount of time in which the black hole can swallow a particular amount of matter). Let's assume ideal conditions.

• there are a lot of parameters, its speed, its angle of penetration, the energy required to do a pipe hole through the Earth from part to part and thermodynamic effects with the geomorphology , etc ; it needs a complex simulation – user46925 Jan 18 '16 at 16:01
• Irradiating does not mean "not radiating". Secondly, the amount of matter devoured per unit of time is limited by the Eddington limit. You might be able to gain some insight reading up on that. – Sanchises Jan 19 '16 at 13:13
• Thanks for an advice and sorry about that mistake, my English isn't that much perfect and I still have a lot to learn. "Irradiating" was a really bad choice of words... – Mr. Numbers Jan 19 '16 at 15:25
• Why doesn't this black hole emit Hawking radiation? Why do you think it will be able to absorb any normal matter? It's much smaller than an atom. – PM 2Ring Mar 18 at 8:24

As a fist approximation we can also assume that the black hole obeys Newtonian dynamics, that is $$F=ma$$ (I know this is now strictly true but it gives us something to work with). In this case the acceleration at earth's surface is just $$a=g$$. As the black hole tumbles towards the earth's centre it it will increases in mass (it literally eats it's way through the earth). However, since $$a=F/m$$ the acceleration will not depend on the mass of the (still small) black hole, but only on the mass of the earth at smaller radious. Assuming constant density (which is wrong) the acceleration would go as $$a = g \frac{r}{R}$$ where $$R$$ is the radios of the earth. As you say the black hole will oscillate between the earth surface through the core and out again.