Mryntu

Set in present day New York City, an unknown spacecraft of alien origin expelled millions of micro blackholes each with the mass of a grape in the earth atmosphere. I like to know what happens if these millions of micro blackholes were to fall on building structures such as skyscrapers, would it trigger an extinction level event?

would it triggers extinction level event?

Since they'd evaporate more or less instantaneously (known as Hawking radiation), releasing energy according to the famous equation beginning E=, the spaceship would last a few microseconds at best, Earth would be fine.

Yes, the aliens in the ship would become extinct.

Black holes evaporate by emitting Hawking radiation

a 1-second-life black hole has a mass of $2.28 cdot 10^5 kg$

A grape has far less mass than that, thus the black hole would evaporate way faster than that.

An intelligent life form dropping micro black holes on Earth would thus quickly annihilate its own bombing squad in a shower of gamma ray, proving that they were not so intelligent as we thought.

The electromagnetic force from one electron on another and the gravitational force of this micro-black hole both follow an inverse square law. A grape about 1.5 cm in radius would have a mass of about 0.015 kg.

When does the gravitational force of the grape exceed the electromagnetic force between electrons ? It's when :

$$frac r R < sqrtfrac 4pi epsilon_0Gm_em_he^2 = 6.3times 10^-8$$

Meaning the black hole would have to pass less than one ten millionth of the distance between electrons to have a significant influence on one. Away from than range the electron will happily go about it's business hardly disturbed at all.

Even if a black hole passes this close the effect is only temporary. You're still nowhere near the event horizon of that black hole and so the electron will, at worst, be pulled away from it's normal motion and after some brief period when the black hole moves away it will simply recombined in some way with the bulk of atoms around it. It might cause a minute amount of damage on a molecular level (even allowing for millions of these micro black holes), but the net effect would be tiny, probably less that someone hitting a wall with their hand.

How about they expell at fraction of c so we take length contraction into question?

You seem to mean that to avoid Hawking radiation evaporation destroying these black holes before they even reach the black hole, they could be ejected at a high fraction of the speed of light.

So how high a speed is needed to avoid them evaporating before they travel 100 meters, assuming your aliens like low level flying ?

The fraction of the speed of light needed is :

$$frac v c > frac 1 sqrt 1 + left( frac Tc L right)^2 $$

Where $L$ is the distance they must travel and $T$ is the lifetime of the micro black hole before it evaporates.

This works out at $frac v c approx 1 - 2times 10^-19$. That's insanely close to the speed of light.

A million grapes of mass 0.015 kg will have a mass of 15,000 kg. But the energy required to get them moving at this insane fraction of the speed of light would be enormous. It equates to a mass about $2times 10^9$ times 15,000 kg. Or to put it another way, the ship firing these micro black holes would need to have a mass-energy of about $3times 10^13$ kg. The asteroid Vesta is substantially larger than this.

So this is actually a small mass in terms of asteroids and you could probably destroy Earth a lot more easily simply by grabbing some handy largish asteroids and sending them on their merry way towards Earth at some modest speed that's easily imparted with your spaceship.

Conclusion :

No need at all to mess around with ultra-relativistic micro-black holes when the universe provides you with much simpler and easy to handle "ammunition" in the form of basic asteroids.