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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?

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closed as unclear what you're asking by Ben Crowell, John Rennie, Jon Custer, honeste_vivere, Yashas Aug 13 '17 at 15:51

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    $\begingroup$ @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. $\endgroup$ – MBN Mar 8 '16 at 17:13
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    $\begingroup$ @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. $\endgroup$ – CuriousOne Mar 8 '16 at 22:51
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    $\begingroup$ @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. $\endgroup$ – MBN Mar 8 '16 at 23:38
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    $\begingroup$ @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. $\endgroup$ – CuriousOne Mar 8 '16 at 23:47
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    $\begingroup$ @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. $\endgroup$ – MBN Mar 9 '16 at 11:13
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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.

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  • $\begingroup$ 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. $\endgroup$ – Ben Crowell Aug 12 '17 at 22:36

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