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We assume that there is an infinite density at the center of a black hole. But we also know that if it was really infinite, it would apply an infinite gravitational force to masses even if they were millions of light years away. So there must be a multivariable calculus equation for a black hole's force field. There must be some boundaries.

However, we also know that some black holes even bend lights, massless particals, so we are also pretty sure somewhere in the equation for some specific conditions there is an infinity. So in the equation, the boundaries must be set by another dimension, another variables we can not observe that are beyond 3 dimensions and space-time compression.

So this is where I got so far. If some variables from another dimension(s) involved, what are they? If not, how a black hole which is assumed to have an infinite density, does not effect us (Earth) infinitely?

Qmechanic
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Alper91
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  • A singularity is simply a point or a set of points where a theory breaks down. There is no expectation among physicists that singularities actually exist in nature. – CuriousOne Mar 08 '16 at 14:15
  • "But we also know that if [density] was really infinite, it would apply an infinite gravitational force..." but the mass is not infinite, and gravity is caused by mass, not by density. – Asher Mar 08 '16 at 16:34
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    @CuriousOne: It is not a point or a set of points. If it were, what space would it be a point of? It curtainly isn't part of the space-time. – MBN Mar 08 '16 at 17:13
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    @MBN: To put it bluntly: a singularity is a simple mathematical error. It doesn't exist in this universe, so discussion whether it is part of a space or not is not physics. Having said that, mathematically singular points/sets are part of the describing MATHEMATICAL space. – CuriousOne Mar 08 '16 at 22:51
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    @CuriousOne: Not in relativity. They are not part of the the discribing mathematical space, in this case the Lorenzian manifold. Thus my objection to calling them points. – MBN Mar 08 '16 at 23:38
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    @MBN: I have no idea where you get that idea from. Of course you can (and do) include the singularity coordinates in the manifold (maps). Just because predicted physical quantities diverge doesn't mean you can't have a map for where they diverge. There is just no meaningful physics at those points. – CuriousOne Mar 08 '16 at 23:47
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    @CuriousOne: That's not true. Can you give a reference (textbook or paper) where the singularities are included as points of the manifold? From what I have been able to gather, there is no satisfactory way to do that. Each proposal can deal with only some singular space-times and omits others. – MBN Mar 09 '16 at 11:13
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    @MBN: $r=0$ is a valid coordinate for the Schwarzschild or Kruskal-Szekeres metric, it's just meaningless to look for physics at that coordinate. There is no coordinate transformation which brings "There ain't no physics here!" down to "Meaningful physics at this junction!". Is that what you mean? Do you expect to find a coordinate transformation like for a sphere where one can express the polar region with a second map to avoid the problem with spherical coordinates? That's not what is happening here. – CuriousOne Mar 09 '16 at 12:59
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    Possible duplicate of Is black hole singularity a single point? –  Aug 12 '17 at 23:06

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The infinities of a singularity apply at the singularity, not everywhere; that's actually part of its nature as "a singularity" within a generally non-singular space. The gravitational acceleration of a massive body increases as $1/r$ (for a point mass, i.e. ignoring shell effects) and $1/r$ is only infinite as you approach $r=0$. Obviously, for very large $r$ the gravitational acceleration is quite small, which as an example is why it takes us here near the edge of the galaxy so long to make an orbit, even though the galaxy is very massive: the galaxy is also very wide (very large $r$) so two factors balance out to a finite (and rather small) acceleration.

Asher
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  • This is completely wrong. A singularity in GR is not defined by infinite gravitational acceleration. The equivalence principle says that we can always make the gravitational acceleration be zero by picking an appropriate frame of reference. Even if you demand a stationary frame of reference, g diverges at the event horizon, not the singularity. –  Aug 12 '17 at 22:36