A Reading suggestion
Hi, cooldude3122,
Thanks for the indication of your level; this is very helpful in trying to give you answers/advice which I hope you will find useful!
0. In future, I urge you to try to write complete sentences. "Blackberry style" posts are inappropriate for discussions of subtle concepts in math/physics!
cooldude3122 said:
so if the point of infinite density is infintessimally small... then it [a black hole] is a point right?
1. Physics deals with physical theories which are expressed in the language of mathematics and compared with experiment and astronomical observation. More precisely, theoretical physicists make specific quantitative predictions which experimentalists can then test. In this way, theories can be ruled out. In the case of our first "best theories" of gravitation, Newtonian gravitation and gtr, it would be more accurate to say that limits on the domain where a given theory is thought to be reliable can be changed by new evidence. Note that gtr is our current gold standard theory of gravitation and has been very extensively tested, with the result that we know a lot about where Newtonian theory breaks down (and where it is still safe to use), and we also know that any useful theory of gravitation must give predictions which are essentially indistinguishable from gtr in all conditions we have yet tested. Consequently, discussions of "gravity" are usually assumed to refer to gtr unless an alternative is specified. In any case
some theory (or class of theories) must be specified in order to have a meaningful discussion.
2. To prevent possible confusion I stress that under the conditions where it is known to be safe to use Newtonian gravitation, this theory gives predictions indistinguishable from gtr, but is much easier to work with, so it makes sense to use it wherever possible. If gtr is ever succeeded by a better theory, similar remarks should hold true for the domain where Newtonian gravitation breaks down, but gtr does not.
3. Strong theoretical considerations strongly suggest that gtr should eventually be found to break down under certain conditions (sufficiently small scales, sufficiently strong gravitaitonal fields).
4. It is true that in some ways black holes can be thought of as the analogs in gtr of the "point masses" of Newtonian gravitation. Nonetheless, a black hole, as this concept is understood in the context of gtr, is
not a "point of infinite density" or even "infinitesimally small".
5. I urge you to read an excellent book by Geroch,
General Relativity from A to B, which is aimed at high school students (or equivalent) and which focuses at conveying by (good!) pictures an accurate intuition for some of the basic features of the black hole concept in gtr, such as the meaning of the "event horizon" in terms of "light cones" attached to each "event" in spacetime. (There are some other good nontechnical books, but this one is exceptionally good and specifically attempts to address the very issues which have confused you.)
cooldude3122 said:
If so, then wouldn't it be a link to another dimension like the tenth or zero dimension or something like that? ...idk if you believe in multiple dimensions...
6. Some theories which have been proposed and which attempt to provide a candidate for the successor theory to gtr as our gold standard theory of gravitation---some of these, such as superstring theory, also attempt to unify gravitation with various other fundamental interactions--- do posit "extra dimensions". I recommend that you study the popular book by Geroch before trying to learn about superstring theory. However, a good popular book on superstring theory is Brian Greene,
The Elegant Universe.
7. Superstring theory has been criticized on the grounds that so far its advocates have apparently been unable to suggest any test feasible with currently forseeable technology which would enable experimentalists to compare it with gtr. Some critics charge that superstring theory advocates have been reduced to claiming the fact that string theory appears to recover gtr in an appropriate limit, just as gtr recovers Newtonian gravitation in an appropriate limit, as a successful "postdiction". IMO these critics have a point, but given the difficulty of the mathematical issues involved, I feel that string theorists have probably not been wasting their efforts. However, I tend to suspect that for the forseeable future string theory may be more valuable in pure mathematics than in physics (because if you extract the original physical motivation, the mathematics remaining is by common consent novel and beautiful), and I note that mathematics developed in order to pursue some "failed physical theory", e.g. knot theory, often turns out to be useful for unforeseen applications, and may even eventually turn out to have applications not very far from the original motivation!
