Nope, micro black holes still not a threat

A while back, I attempted to allay your fears by explaining why the Large Hadron Collider is not a threat to humanity, because even if scientists did create micro black holes, they would evaporate before they could grow to devour the Earth.

Now a group of physicists is claiming that black holes may not evaporate as quickly as we thought (via FoxNews.com)

"We conclude that ... the growth of black holes to catastrophic size does not seem possible. Nonetheless, it remains true that the expected decay times are much longer (and possibly >> 1 second) than is typically predicted by other models," the three state in a brief paper posted at the scientific discussion Web site ArXiv.org.

First, a check on journalistic integrity. Compare the bolded statement with the FoxNews.com headline:

"Scientists Not So Sure 'Doomsday Machine' Won't Destroy World"

I think it's just Reporters who are Not So Sure.

FoxNews.com can think of a few other things that didn't seem possible once — the theory of continental drift, the fact that rocks fall from the sky, the notion that the Earth revolves around the sun, the idea that scientists could be horribly wrong.

It's happened before, that scientists have been dead wrong about something, and I'll grant that the physicists' article is very difficult reading for a layman (and not exactly light reading for someone with a Ph.D. either), however, unless all of our current understanding about physics is completely wrong, here's why we're still not in trouble.

The rate at which a black hole grows depends on its mass. (Kind of like how a 200-lb man can eat a lot more than a 20-lb kid.) The growth rate is therefore exponential, and I've already done the figurin' for a very simplified model so you'll just have to trust me that the expression is something like:

M = e^{7.06x10-17t - 10.8} (grams per second)

where M is the mass of the black hole in grams, t is the elapsed time in seconds, and the initial mass is the smallest mass theoretically possible for a black hole, 2 x 10^-5 g (about 10¹⁹ times the mass of a heavy particle like a proton), and assuming accretion at 100% efficiency. Again, this is a very simplified picture of black hole accretion, but it gets the point across.

If scientists are able to create a micro black hole with an initial mass of approximately 2 x 10^-5 g, let's take a look at the micro black hole's mass (up to 10 decimal places) after different increments of time:

t = 1 second
M = 2.0399503411 x 10^-5 g

t = 1 minute
M = 2.0399503411 x 10^-5 g

t = 1 hour
M = 2.0399503411 x 10^-5 g

t = 1 day
M = 2.0399503411 x 10^-5 g

t = 1 year
M = 2.0399503457 x 10^-5 g (starting to change more noticeably)

t = 100 years
M = 2.0399507948 x 10^-5 g

t = 1000 years
M = 2.0399548778 x 10^-5 g

t = 1 million years
M = 2.0444920349 x 10^-5 g

t = 1 billion years
M = 1.8855892509 x 10^-4 g (now, we're cookin')

t = 5 billion years
M = 1.3764393726 g

Assuming no evaporation, by the time the Earth is incinerated by our dying Sun, the micro black hole will have grown to a mass of only 1.38 grams.

The physicists claim in their article that a black hole's mass would have to exceed 10⁸ grams before its growth rate would overcome the evaporation rate, but even if they're completely wrong about black hole lifetimes, the micro black hole would still be less than 2 grams in mass by the time life on Earth is extinguished.

Must be a slow news day.