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Any question about Black Holes or time travel seems to have some untested theory or incredibly complicated and prohibitively expensive solution, this question is no different.

While the second half of this 2 part question can be a guess, it would be great if the first half could be estimated and calculated with a reasonable level of precision.

Cornell University has this interesting article: "Can you see the future as you fall into a black hole?", and many have heard of the question: "What would happen if I fell through the Earth?".

This question is basically the same idea, but as it applies to a specially designed Black Hole.

Sort of like asking about the mass of a sphere with two cones removed from it, but I'm more concerned about gravity (or minimizing it in the center) and the predicted difference (if significant) between this shape and a conventional (flattened spheric) Black Hole.

Fall through the Earth

If we could do some (admittedly impractical and expensive) mining, or construct a force field or, create a gravity bottle the shape of two Erlenmeyer flasks placed mouth to mount inside a Black Hole ...

2 Erlenmeyer flasks Cone and Tunnelled Black Hole

Question 1: Could one design a shape that could be carved out of a Black Hole such that you could walk or fly through the center and back out without being trapped or crushed by gravity?

Loose assumptions (so it's easier to design, solve, and use):

  • The diameter of the tunnel can be a few 1000 meters or more to allow any heatshield and antiradiation lining to minimize the amount of protective plating on your spacecraft.

  • The chosen length of the cone connecting tunnel versus the size of the two funnels needs to remove enough mass to reduce the gravity to no greater than 2g throughout one's journey through the center.

    Gravity far away from you (like externally at the equator) can be much higher (it's not like the "fall through the Earth question" says that the hole affects Earth's gravity significantly) It also mentions that in the center it's zero gravity.

    If it could never be practical for a manned spacecraft to travel through the center then I guess it could be useful if the 2g constraint was increased 5 to 50 times greater, but only if the increased gravity would increase the effect (in the event that the amount of central gravity would make any difference to question 2).

  • The total mass and radius of the Black Hole can be fairly large, if we're not concerning ourselves as to how we'll shovel all that matter out why worry about those parameters either. The answerer is welcome to pick a convenient size to make the math easier and it would be helpful if this modified Black Hole made question 2 easier to figure out (to provide a useful / measurable effect).

So I not trying to limit the design too much.

Question 2: Would such a portal (or sphere with two cones connected by a tunnel) allow spacetime effects to be studied (either mathematically, or using a probe / spacecraft) and would it be expected to maintain most of the spacetime effects of a similar Black Hole that was not so modified?

Artist's conception of finished product:

Falling into time

Here's a useful illustration of an outgoing null cone from "Bondi-Sachs Formalism" by Thomas Mädler and Jeffrey Winicour where they write:

"The Bondi-Sachs formalism of General Relativity is a metric-based treatment of the Einstein equations in which the coordinates are adapted to the null geodesics of the spacetime. It provided the first convincing evidence that gravitational radiation is a nonlinear effect of general relativity and that the emission of gravitational waves from an isolated system is accompanied by a mass loss from the system. The asymptotic behaviour of the Bondi-Sachs metric revealed the existence of the symmetry group at null infinity, the Bondi-Metzner-Sachs group, which turned out to be larger than the Poincare group".

An outgoing Null Cone coincides with the shape I guess would need to be removed to reduce the gravity at the surface of the spheric.

Thanks for your comments and answers (corrections welcome).

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    $\begingroup$ There are several misconceptions in your question. A black hole isn't a solid body. All of its mass is concentrated in a tiny region at the centre, possibly a mathematical point, but certainly smaller than an atom. Also, when you're falling you don't feel gravity, although can experience tidal force if the gravity is strong. Maybe you could ask about a neutron star instead, but even there your conical tunnels are impossible because nothing is strong enough to stop them from collapsing. $\endgroup$ – PM 2Ring Dec 22 '17 at 22:23
  • $\begingroup$ Hi, you ask for corrections, but in my case personal opinion would better describe it. Why do you think the centre of a black hole is physically anything remotely spherical like Earth? It's a singularity, any assumptions regarding its shape are based on the world you see around you, but I strongly doubt if a singularity could be described in those terms. $\endgroup$ – user179430 Dec 22 '17 at 23:36
  • $\begingroup$ @safesphere We don't have a complete theory of quantum gravity, so we don't have a way to predict what the centre of a BH is really like. It might be a mathematical singularity, but many people suspect that quantum effects prevent that. GR says that a body falling into a BH crosses the event horizon in finite proper time, and swiftly proceeds to the centre. Sure, a pure Schwarzschild BH is a vacuum solution which requires no matter, by that's hardly a physical model of a real BH, is it? I totally agree that you can't extract useful information from the interior of a BH, though. $\endgroup$ – PM 2Ring Dec 23 '17 at 0:00
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    $\begingroup$ In your last quote, it is just a blanket description for the event horizon which defines the black hole volume, beyond which all matter entering is trapped. You are asking about mathematics to be applied on this general relativity object. There is no way any matter can be used to cut/manipulate etc the black hole geometry. As it gets to the event horizon it disappears, is irrevocably caught by the gravitational field of the black hole so your question has no meaning within the mathematics . After all a black hole is a mathematical construct of General Relativity. You cannot manipulate this. $\endgroup$ – anna v Dec 23 '17 at 4:32
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    $\begingroup$ The mathematics has to be consistent, notIt is a a la cart. The mathematics of General Relativity for the black hole do not allow solutions as you imagine, so your questions cannot be answered. Answers must be within the solutions of equations with physical boundary conditions imposed. The boundary conditions you try to impose are contradictory to the functional form of the solutions. When the solution says : "any matter is drawn to the central singularity" you cannot draw shapes and cut like a cake, the mathematics is already fixed . $\endgroup$ – anna v Dec 23 '17 at 4:47
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You are basically asking: can one go through the hole in a donut-shaped black hole? The answer seems to be no.

Drilling holes through black holes is not just hard but is conceptually impossible: they are not solid things, but rather regions of spacetime curvature. However, toroidal black holes have been seriously studied by theoretical physicists. One can certainly imagine making one by (say) taking a lot of heavy mass, distribute it in a ring and compressing it until it should implode in a torus-shaped black hole. The question is what happens then, and whether one can pass through the central hole.

The cool (or deeply annoying thing) is that we are subject to "topological censorship" (paper). This means that in an asymptotically flat spacetime (whatever weird spacetime structures we care about are localised inside an otherwise flat universe) with a well-defined direction of time and obeying the null energy condition, a possible spacetime path of an observer going from the infinite past to the infinite future can be smoothly deformed into a trivial path at infinity. (Paths falling into singularities are not allowed paths)

For black holes with holes through them, this means that there are no valid ways of travel through the central hole and coming out on the other side. The reason is that such a path cannot be smoothly deformed into a path that doesn't pass through the black hole. Note that this nicely sidesteps the question of what the singularity is shaped like: we just need to know that there is an event horizon (indicating that if you cross it you will not come out) and what shape it has.

What seems to actually happen if one were to make my above scenario with compressing a toroidal mass is that once it becomes a black hole the event horizon spreads across the ring "faster than light", preventing anybody from getting through. It is allowed to do that since a event horizon isn't a physical thing but something that is defined by how it prevents certain things from being seen or observers to move.

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  • $\begingroup$ Thanks for your reply. Instead of a toric shape mathworld.wolfram.com/Torus.html we could refer to it (incorrectly) as similar to a spherical ring (napkin ring): mathworld.wolfram.com/SphericalRing.html - an important distinction is that the holes are countersunk and the mass removed from the entrances decreases the surface gravity, holding it comparable to the gravity in the center. The article "Bumpy Black Holes": arxiv.org/abs/1410.4764 on page 11, Figure 5a, describes a "(+)1-branch black hole at j = 1.13, close to the transition to a black ring". Still searching. $\endgroup$ – Rob Dec 29 '17 at 4:19

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