What is the gravity and effect of a Black Hole with two connected cones cut from it?

Question

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.

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 ...

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:

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".

Thanks for your comments and answers (corrections welcome).

Answer 1

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.