Gravity Increase With Small-Massive Objects?

Question

I'm pretty sure that I understand the concept, but I'd like to be sure about this. My question pertains to how gravity increases as the mass of an object is compacted into a smaller and smaller space (i.e. a black hole). Does the gravity increase because the space-time distortion becomes steeper and steeper as the object becomes smaller?

This is how I'm picturing it (though its probably way out of scale!). Say there is an object that is as large as the center of a plate that has a mass of x which distorts space-time to a curvature equal to the curved edges of a plate. As one may clearly see this is not too steep of a curvature. On the other hand, if an object such as a shot glass has the same mass of x and is the size of the bottom of the shotglass then the space-time distortion of the object is equal to the sides of the glass. Thus, the shotglass object requires more energy to escape from inside of the glass than the energy required for an object to escape the plate. Am I correct?

Answer 1

Who am I, or anyone else here on yahoo answers to say that you are incorrect, your thoughts sound interesting, and are valid to you.

This is the way that I think of gravity increasing with Small Massive Objects, such as a quantum singularity for example.

If you could picture gravity in-waves as a string of energy and compared to a common thread, and you could also picture two common bicycle tires which we could compare to as uncompressed mass, then between two spinning bicycle tires, there is only a small limited amount of space in which a small limited amount of strings could traverse between two tires spinning together.

as the space becomes compressed with in the quantum singularity, and the mass shrinks in size, the diameter of bicycle tires then becomes wider and narrower and resembles wide racing tires on the automobiles at the Indianapolis 500, and with regard given to the width, and with consideration to the in-waves which remain the same, and which in this case represent the thread, then you can easily understand that if two spinning racing tires were spinning together, they would suck a vast many more threads between the surface area, thus increasing the in-wave acceleration while the mass appears to shrink in size.

Answer 2

Outside a spherical object, the strength of gravity goes as 1/r^2, where r is the distance to the center of the massive object.

However, INSIDE a spherical object, the gravity goes as r, where is r is the distance to the center.

Now, let's say you have a star with 5 solar masses (5 times the mass of our Sun). At a distance of 10 million miles, the gravity will have a certain strength. If you are 10 million miles from a black hole with 5 solar masses, the gravity will be the same.

For a star and a black hole that have the same mass, you will only see different effects inside the radius of the star. Since the star has a large volume, as you approach, the gravity will increase until you reach the surface, then it will decrease to zero as you travel to the center. However, a black hole has no size at all, so the gravity will increase without bound as you approach it.

Answer 3

Your explanation is basically correct. Space-time curvature does depend on mass density. The Schwartschild solutions to Einstein's equations of General Relativity show that if the mass density exceeds a certain value, the space-time curvature must converge to an infinitesimal point (singularity).