What If You Were Turned Into A Black Hole?

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If you were a black hole how big would you be and how long would you last?

This post explores the explosive facts surrounding micro black holes.

A VERY BRIEF PRIMER ON BLACK HOLES

A basic property of matter is that it generates gravity, a force that attracts all other matter towards it. The strength of this force increases with increasing mass and it decreases with increasing distance (it decreases as the inverse square of the distance to be more exact).

Take a largish lump of matter like the Earth and throw a ball up into the air. It will of course come back down due to the gravitational force. Throw it harder and the ball will go higher but still come back down.

The higher this ball goes the weaker the gravitational force gets so if you throw it fast enough the ball will still always slow down but it will never reach zero velocity and it will never come back. This is known as the escape velocity.

The escape velocity for the Earth is about 11 kilometres per second. For a larger planet like Jupiter the escape velocity is about 60 kilometres per second. For our local star, the Sun, the escape velocity is about 620 kilometres per second.

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Public domain image.}

Take this thought process to the extreme and imagine a body so massive that the escape velocity becomes greater than the speed of light. This would be a naive and simplistic Newtonian physics black hole and it was first thought up by an English clergyman John Michell back in 1784.

Real black holes are more complicated and more interesting than this first naive conception.

First, the force of gravity in such a massive body would collapse the matter down into something more dense than a neutron star and is known as a 'singularity'. The term singularity was coined I presume because with a black hole you are trying to divide by the number zero and the current mathematical theories break down because of this.

HOW BIG WOULD YOU BE?

A real black hole requires the mass of at least 5 solar masses or so and even so the event horizon (the Schwarzschild Radius) of these object is surprisingly small.

The equation for the Schwarzschild Radius is r = 2GM/c² where G is the gravitational constant, M is the mass of the object and c is the speed of light. We will use this equation to calculate the size of a few types of black holes.

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WHAT IF THE SUN WERE A BLACK HOLE?

Plugging in the numbers for the Sun (M = 2 x 10³⁰ kg) gives us a black hole radius of about 3,000 metres. Imagine that, the mass of the entire Sun packed into something that small.

This is the size of the event horizon, the radius at which not even light can escape. The actual size of the object inside the event horizon will probably be even smaller than that but that is a topic for another post.

WHAT IF THE EARTH WERE A BLACK HOLE?

Imagine then that the Earth for some reason was compressed into a black hole. How big would it be? Plugging in the numbers for the Earth (M = 6 x 10²⁴ kg) gives us a black hole radius of about 9 millimetres.

Not very large at all. In fact it would be about the size of a head of a pin.

WHAT IF A HUMAN WERE A BLACK HOLE?

Now imagine that a human could be compressed into a black hole. Let's assume a mass of 70 kilograms.
Plugging in the numbers gives us a black hole radius of about 1 x 10^-25 metres.

A proton has a charge radius of 0.88 femtometres which is 8.8 x 10^-16 metres. So a proton would be far larger than a human turned into a black hole.

HOW LONG WOULD YOU LAST?

Black holes are not forever. Due to the quirks of quantum mechanics black holes are theorized to "evaporate" in a process called Hawking radiation (named after Stephen Hawking).

The process is very slow and the time required to evaporate a stellar black hole would be measured in many multiples of the lifetime of the current Universe.

A rough equation for the lifetime of a black hole has been worked out in the Wikipedia page for black holes and is as follows:

_{equation reference link}

If the Sun were turned into a black hole the equation tells us that it could be expected to evaporate in 2 x 10⁶⁷ years. Basically long enough that no one will be around to check if your math is correct.

However, the smaller a black hole gets, the faster it will evaporate. When a black hole starts getting tiny this evaporation rate continues to grow eventually becoming ferocious and ending in a large explosive event.

If a human were turned into a black hole the same equation predicts a lifetime of only about 0.03 nanoseconds (3/100^th of a billionth of a second).

This means that all of that mass (70 kg) would be converted into energy in a time scale roughly comparable to the reaction time of a nuclear weapon. However the mass to energy conversion ratio would be 100% in the case of a micro black hole and the blast would be tremendous.

In an earlier post (One Gram Killed Hiroshima), I worked out that 2.3 kg of mass disappeared in the 50 megaton Tsar Bomba explosion.

A human black hole explosive event would therefore be about 30 times more powerful than the Tsar Bomba atomic weapon.

Keep your distance.

_{Image credit: United States Department of Energy link
Public domain image.}

CLOSING WORDS

Micro black holes are postulated to have been produced during the first few moments of the Big Bang when densities and pressures were still extremely high. These tiny black holes are theorized to be reaching the ends of their expected lifetimes sometime in our current era and the final 'evaporation' event would look a lot like a gamma ray burst.

Unfortunately no evidence of their existence via gamma ray bursts has been found (yet). Maybe they are all gone or maybe they are still evaporating away quietly somewhere nearby within our galaxy just waiting to make for a very bad day for anyone happening to be living nearby.

Thank you for reading my post.

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