Solving Confusion About Black Holes, Schwarzschild Radius & Time Dilation

[arkantos]

According to the theory, every mass has a Schwarzschild radius associated. Any object whose radius is smaller than its Schwarzschild radius is called a black hole.
So in principle is possible to create mini-black holes, it is just a fact of matter condensed.
Those mini black holes have their event horizon ecc, and despite their should evaporate in a infinitesimal amount of time, they have the same capacity to curve space time in the same fashion regular black holes do.
But I guess there is something wrong with my understanding of the theory, because:
Space time curvature is progressive for astronomical objects, for example Neutron Stars curve space-time 'more deeply' as they get closer the their Schwarzschild radius, and eventually becoming black holes.
Now, according to this logic, the more an object get closer to its SH radius, the more it curves space-time. Is this statement applicable to objects on the Earth? Ab absurdum, does an atomic nucleo curve space time more than a big and heavy rock?

 

[PAllen]

The curvature at the event horizon is actually inversely proportional to the mass - the smaller the BH, the larger the curvature at its event horizon. On the other hand, a proton, for example, is actually almost 40 orders of magnitude larger in radius than a BH of the same mass, so it is 'enormously further from being a BH' than is the earth. Thus the curvature it produces is wholly insignificant.

 

[arkantos]

The curvature at the event horizon is actually inversely proportional to the mass - the smaller the BH, the larger the curvature at its event horizon. On the other hand, a proton, for example, is actually almost 40 orders of magnitude larger in radius than a BH of the same mass, so it is 'enormously further from being a BH' than is the earth. Thus the curvature it produces is wholly insignificant.

okay, thanks for the answer.
So now I have another question: from the point of view of an observer, when an object crosses the event horizon of a super massive black hole, which density is low,it will be frozen immediately right?
According to the observer the object is already frozen in time even if the curvature at the event horizon, and so the gravitational pull, it's not extreme, right?

 

[PeroK]

okay, thanks for the answer.
So now I have another question: from the point of view of an observer, when an object crosses the event horizon of a super massive black hole, which density is low,it will be frozen immediately right?
According to the observer the object is already frozen in time even if the curvature at the event horizon, and so the gravitational pull, it's not extreme, right?

An observer outside the EH never receives a light signal from an object crossing the horizon.

There is, strictly speaking, no gravitational "pull" in GR. There is, however, a force required to hover outside the EH. That force increases without limit as you approach the EH.