Does black holes exist all around us?

[wavingerwin]

I read Wikipedia about black hole and interpreted it as such: that black holes exist all
around us, most of them are very, very small.

Suppose we have a drinking water glass (just suppose its mass is 10kg)
hence at radius 1.48 E-26 m (far smaller than even the radius of an electron)
there exists a black hole at the centre of mass of the glass.
(by the calculation done using escape speed equation, plugging in the speed of
light as the escape speed, we can get the value of r, in which any particle
even in the speed of light cannot escape from.)

because by calculation, the escape speed;v of any object inside the
radius will be greater than the speed of light hence it cannot escape, even light cannot.

so there is a tiny black hole at the centre of the glass. Am i right? please explain if not.

Thank you

here's the extract of the article in http://en.wikipedia.org/wiki/Black_hole

consider a heavy object of mass M centered at the origin. A second object with mass m starting at distance r from the origin with speed v, trying to escape to infinity, needs to have just enough kinetic energy to make up for the negative gravitational potential energy, with nothing left over:

mv²/2 - GMmr^-1 = 0

That way, as it gets closer to r=infinity it has less and less kinetic energy, finally ending up at infinity with no speed.

This relation gives the critical escape velocity v in terms of M and r. But it also says that for each value of v and M, there is a critical value of r so that a particle with speed v is just able to escape:

r = 2GM/v²

When the velocity is equal to the speed of light, this gives the radius of a Newtonian dark star, a Newtonian body from which a particle moving at the speed of light cannot escape. In the most commonly used convention for the value of the radius of a black hole, the radius of the event horizon is equal to this Newtonian value.

r_{Schwarzschild} = 2GM/c²

 

[Danger]

Welcome to PF, V.
I think that microscopic black holes are still open for conjecture. For a 'real' black hole, you need a body of at least 3.2 Solar masses in order for the gravitational collapse to take hold. The most likely place for that to occur is in a red giant star that goes supernova. If SpaceTiger is still around here, he's definitely the go-to guy for this.

 

[atyy]

Suppose we have a drinking water glass (just suppose its mass is 10kg)
hence at radius 1.48 E-26 m (far smaller than even the radius of an electron)
there exists a black hole at the centre of mass of the glass.

No, the meaning of the radius you calculated is that if the mass of the glass were concentrated into a volume less than that radius, then a black hole will form.

 

[Nabeshin]

No, the meaning of the radius you calculated is that if the mass of the glass were concentrated into a volume less than that radius, then a black hole will form.

Right. As you shrink your radius you also shrink your mass, so there is no point at which there is a black hole inside any object that, well, isn't a black hole.

 

[wavingerwin]

mass of the glass were concentrated into a volume less than that radius, then a black hole will form.

I see.. it makes good sense for me
So for a black hole to exist, the 'critical radius' (of which any object cannot escape from
without moving at v>c) must be bigger than the volume of the object itself (which creates the black hole).