Interstellar Singularity Scene

[Pierpont Oldham]

Acommon misunderstanding is that there is just one type of black hole, namely a Schwarzschild black hole. There are actually many types, which differ topologically (the number of dimensions and underlying "shape" of space near to the black hole) and metrically (the class of solution to Einstein's field equations, a highly nonlinear tensor equation and the defining mathematical construct of general relativity).

Most likely, the black hole in Interstellar is a Kerr black hole. This is an axisymmetric black hole with nonzero angular momentum. In lay terms: it rotates. Having read some of the source material related to Kip Thorne's involvement with the film, as well as what they were trying to achieve with the visuals, I would put my money on a Kerr black hole. This is also consistent with the fact that planets seem to be orbiting this black hole!

Coop's experience inside the black hole is also consistent with the theory. A Kerr black hole is not nearly as "destructive" as a standard, non-rotating Schwarzschild black hole. In particular, the singularity is ring-shaped with a nonzero radius and objects (particles, really) can travel past the event horizon and through the ring without intersecting the singularity itself. Inside the ring, one experiences the Carter effect (named after physicist Brandon Carter), in which one can move freely in time as one would in space. That seems to be Coop's "tesseract" in a nutshell!

The black hole in Interstellar was not purely natural, but had been created or modified by a stupendously powerful and advanced civilization. As such, there is not much point trying to analyse the properties of its interior in terms of our current understanding of physics.

The film makes it clear that the black hole engineers can manipulate spacetime, which enabled the time-travel effects seen by the characters. Cooper and TARS surmise that the tesseract was created by the builders, as an environment in which Cooper could survive and

As for how Cooper left: In our current understanding, once matter crosses the event horizon of a black hole, it can't get out again. We can only assume that with a sufficiently advanced technology, the black hole builders knew of a loophole which allowed him to get out.

I'll address question #1 first. I think this one has to do with the fact that Cooper and TARS actually reached one of the singularities inside the black hole, where TARS was able to gather the needed "quantum data" (my answer here covers why this was necessary), and that was the point where they were rescued from the black hole by the "tesseract" which had been created by the beings living in the higher spatial dimension. This bit of dialogue between Cooper and Romilly on Mann's planet is key:

ROMILLY: Beyond the horizon is a complete mystery - who's to say there isn't some way the probe can glimpse the singularity and relay the quantum data? If he's equipped to transmit every form of energy that can pulse - X-ray, visible light, radio -

As explained in Ch. 26 of The Science of Interstellar by physicist Kip Thorne (who was the movie's science consultant), a realistic version of a rotating black hole like the one in Interstellar would actually have more than one singularity. There is of course the one at the center, which Thorne says would likely be a type of singularity known as a BKL singularity. This type of singularity would rip apart all objects with ever-more-violent oscillations in the tidal forces, which are gravitational forces that act differently on different parts of an extended object (an astronaut's feet being pulled more strongly than his head, for example) and therefore have the effect of stretching and squeezing it. The wiki article on the BKL singularity only talks about it in the context of the Big Bang, but you can look at this article for a discussion of how BKL singularities would apply to black holes.

In addition to the central singularity, theoretical analysis suggest that for rotating black holes there'd be two others, which Thorne labels the "infalling" and "outflying" singularities. These occur when, due to the particular way that time dilation occurs inside the black hole, waves and matter which fell into the black hole at many different times will converge at the "inner horizon" at the same moment--this is a second horizon found in rotating black holes below the outer event horizon, which is not predicted to be present in non-rotating, uncharged black holes (the inner horizon is also often referred to as the Cauchy horizon, and is also theoretically predicted to be present in non-rotating but charged Reissner-Nordstrom black holes). From what I have read elsewhere, the fact that there is a type of singularity here is related to the fact that electromagnetic and gravitational waves become infinitely blue-shifted at the horizon, meaning their wavelength approaches zero as they approach it--this is mentioned for example in the section "Penrose diagram illustrating the cause of mass inflation" at the bottom of this page.

However, unlike the central singularity, these two singularities at the inner horizon may be "gentle" ones in the sense that not only can individual particles theoretically pass through them and continue on the other side, but the period when the tidal forces become really large might be brief enough that they'd only distort the relative positions of the atoms in an object by a finite amount, an amount which might not be enough to rip apart a solid object like a human. Ultimately though, physicists can't really say what would happen when crossing these singularities even from a theoretical perspective, because the theory they use to analyze tidal forces and other spacetime distortions, Einstein's theory of general relativity, is expected to become inaccurate in regions of spacetime with energy densities that reach a scale known as the Planck scale, and in these regions it's thought that a theory of quantum gravity would be needed to make accurate predictions (string theory is an attempt to create such a theory, but it's incomplete).

If you fall into a spinning black hole such as Gargantua, lots of other stuff inevitably will fall in after you: gas, dust, light, gravitational waves, and so forth. That stuff may take millions or billions of years to enter the hole as seen by me, watching from outside. But as seen by you, now inside the hole, it may take only a few seconds or less, due to the extreme slowing of your time compared with mine. As a result, as seen by you this stuff all piles up in a thin sheet, falling inward toward you at the speed of light, or nearly the speed of light, or nearly the speed of light. This sheet generates intense tidal forces that distort space and will distort you, if the sheet hits you.

The tidal forces grow to become infinite. The result is an "infalling singularity" ... governed by the laws of quantum gravity. However, the tidal forces grow so swiftly (Poisson and Israel deduced) that, if they hit you, they will have deformed you by only a finite amount at the moment you reach the singularity. ... Because your body has been stretched and squeezed by only a finite net amount, when you reach the singularity, it is conceivable you migh survive. (Conceivable but unlikely, I think.) In this sense, the infalling singularity is far more "gentle" then the BKL singularity. If you do survive, what happens next is known only to the laws of quantum gravity.

In retrospect, this singularity should have been obvious. It is an outflying singularity that grows as the black hole ages, just like the infalling singularity grows. It is produced by stuff (gas, dust, light, gravitational waves, etc.) that fell into the black hole before you fell in ... A tiny fraction of that stuff is scattered back upward toward you, scattered by the hole's warpage of space and time, much like sunlight scattered off a curved, smooth ocean wave, which brings us an image of the wave.

(If anyone knows enough physics to follow any of the details, the 2012 paper discussing the outflying singularity is here--there wasn't much I could understand, but if you look at the little primer here on Penrose diagrams for different types of black holes, you can then compare with the authors' Penrose diagram for a realistic rotating black hole in Fig. 4 on p. 17 of the paper, which shows the infalling singularity as a red dotted line, and the outflying singularity as a solid red line labeled 'Shockwave'. Also note that the "Discussion" section on p. 18 talks about comparing "two different types of null singularity that develop at the inner horizon", confirming that this is where these two singularities are located.)

The "tesseract", meanwhile, is supposed to be a piece of technology created by the beings (possibly descended from humans) who live in the extra spatial dimension, the "bulk". This idea of an extra extended spatial dimension is based on a real physics theory, the Randall-Sundrum model--see my discussion in this answer for more details. The tesseract is shaped like a four-dimensional hypercube (that's what the word 'tesseract' means, in fact), so each of its "faces" is a 3D cube, just like each face of a 3D cube is a 2D square. In ch. 29 Thorne describes how the tesseract can "dock" one of its faces to our ordinary 3D space, which in the Randall-Sundrum theory is a 3D brane sitting in the 4D space of the bulk (for anyone familiar with the classic "math fiction" story Flatland, I think this docking of a higher-dimensional structure with our space is meant to be analogous to how the 3D sphere was able to materialize in the 2D universe by having one of its cross-sections in the 2D plane). Also, at the end of ch. 28, Thorne indicates that Cooper entered the tesseract at a point right along the outflying singularity (the fact that he and TARS passed through the outflying singularity was necessary to the plot since this allowed them to gather the "quantum data" about the singularity--the other answer of mine I linked to above discusses this as well). Quoting from ch. 28:

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