Skip to comments.Mathematicians Disprove Conjecture Made to Save Black Holes
Posted on 05/19/2018 7:14:18 AM PDT by LibWhacker
Nearly 40 years after it was proposed, mathematicians have settled one of the most profound questions in the study of general relativity. In a paper posted online last fall, mathematicians Mihalis Dafermos and Jonathan Luk have proven that the strong cosmic censorship conjecture, which concerns the strange inner workings of black holes, is false.
I personally view this work as a tremendous achievement a qualitative jump in our understanding of general relativity, emailed Igor Rodnianski, a mathematician at Princeton University.
The strong cosmic censorship conjecture was proposed in 1979 by the influential physicist Roger Penrose. It was meant as a way out of a trap. For decades, Albert Einsteins theory of general relativity had reigned as the best scientific description of large-scale phenomena in the universe. Yet mathematical advances in the 1960s showed that Einsteins equations lapsed into troubling inconsistencies when applied to black holes. Penrose believed that if his strong cosmic censorship conjecture were true, this lack of predictability could be disregarded as a mathematical novelty rather than as a sincere statement about the physical world.
Penrose came up with a conjecture that basically tried to wish this bad behavior away, said Dafermos, a mathematician at Princeton University.
This new work dashes Penroses dream. At the same time, it fulfills his ambition by other means, showing that his intuition about the physics inside black holes was correct, just not for the reason he suspected.
In classical physics, the universe is predictable: If you know the laws that govern a physical system and you know its initial state, you should be able to track its evolution indefinitely far into the future. The dictum holds true whether youre using Newtons laws to predict the future position of a billiard ball, Maxwells equations to describe an electromagnetic field, or Einsteins theory of general relativity to predict the evolution of the shape of space-time. This is the basic principle of all classical physics going back to Newtonian mechanics, said Demetrios Christodoulou, a mathematician at ETH Zurich and a leading figure in the study of Einsteins equations. You can determine evolution from initial data.
But in the 1960s mathematicians found a physical scenario in which Einsteins field equations which form the core of his theory of general relativity cease to describe a predictable universe. Mathematicians and physicists noticed that something went wrong when they modeled the evolution of space-time inside a rotating black hole.
To understand what went wrong, imagine falling into the black hole yourself. First you cross the event horizon, the point of no return (though to you it looks just like ordinary space). Here Einsteins equations still work as they should, providing a single, deterministic forecast for how space-time will evolve into the future.
Lucy Reading-Ikkanda/Quanta Magazine
But as you continue to travel into the black hole, eventually you pass another horizon, known as the Cauchy horizon. Here things get screwy. Einsteins equations start to report that many different configurations of space-time could unfold. Theyre all different, yet they all satisfy the equations. The theory cannot tell us which option is true. For a physical theory, its a cardinal sin.
The loss of predictability that we seem to find in general relativity was very disturbing, said Eric Poisson, a physicist at the University of Guelph in Canada.
Roger Penrose proposed the strong cosmic censorship conjecture to restore predictability to Einsteins equations. The conjecture says that the Cauchy horizon is a figment of mathematical thought. It might exist in an idealized scenario where the universe contains nothing but a single rotating black hole, but it cant exist in any real sense.
The reason, Penrose argued, is that the Cauchy horizon is unstable. He said that any passing gravitational waves should collapse the Cauchy horizon into a singularity a region of infinite density that rips space-time apart. Because the actual universe is rippled with these waves, a Cauchy horizon should never occur in the wild.
As a result, its nonsensical to ask what happens to space-time beyond the Cauchy horizon because space-time, as its regarded within the theory of general relativity, no longer exists. This gives one a way out of this philosophical conundrum, said Dafermos.
This new work shows, however, that the boundary of space-time established at the Cauchy horizon is less singular than Penrose had imagined.
Dafermos and Luk, a mathematician at Stanford University, proved that the situation at the Cauchy horizon is not quite so simple. Their work is subtle a refutation of Penroses original statement of the strong cosmic censorship conjecture, but not a complete denial of its spirit.
Building on methods established a decade ago by Christodoulou, who was Dafermoss adviser in graduate school, the pair showed that the Cauchy horizon can indeed form a singularity, but not the kind Penrose anticipated. The singularity in Dafermos and Luks work is milder than Penroses they find a weak light-like singularity where he had expected a strong space-like singularity. This weaker form of singularity exerts a pull on the fabric of space-time but doesnt sunder it. Our theorem implies that observers crossing the Cauchy horizon are not torn apart by tidal forces. They may feel a pinch, but they are not torn apart, said Dafermos in an email.
Because the singularity that forms at the Cauchy horizon is in fact milder than predicted by the strong cosmic censorship conjecture, the theory of general relativity is not immediately excused from considering what happens inside. It still makes sense to define the Cauchy horizon because one can, if one wishes, continuously extend the space-time beyond it, said Harvey Reall, a physicist at the University of Cambridge.
Dafermos and Luk prove that space-time extends beyond the Cauchy horizon. They also prove that from the same starting point, it can extend in any number of ways: Past the horizon there are many such extensions that one could entertain, and there is no good reason to prefer one to the other, said Dafermos.
Yet and heres the subtlety in their work these nonunique extensions of space-time dont mean that Einsteins equations go haywire beyond the horizon.
Einsteins equations work by quantifying how space-time changes over time. In mathematical language, it takes derivatives of an initial configuration of space-time. In order for it to be possible to take a derivative, space-time has to be sufficiently smooth free of discontinuous jumps. Dafermos and Luk indicate that while space-time exists beyond the Cauchy horizon, this extended space-time isnt smooth enough to actually satisfy Einsteins equations. Thus, even with the strong cosmic censorship proven false, the equations are still spared the ignominy of outputting nonunique solutions.
It makes sense to talk of the Cauchy horizon; however, you cant continue beyond it as a solution of Einsteins equations, said Reall. Theyve offered pretty convincing evidence that that is true, in my opinion.
You could think of this outcome as a disappointing compromise: Even though you can extend space-time beyond the Cauchy horizon, Einsteins equations cant be solved. But its precisely the fact that this middle ground seems to exist that makes Dafermos and Luks work so interesting.
This is people really discovering a new phenomenon in the Einstein equations, said Rodnianski.
Correction: This article was updated on May 18, 2018, to reflect that it has been 40 years since Roger Penrose proposed the strong cosmic censorship conjecture, not 60 years.
Sheldon and I hate it, when this happens!:)
Isn’t it Racist to call something a “Black Hole”??
“To understand what went wrong, imagine falling into the black hole yourself. “
Trust me, I do that every day.
Yes for one thing you need to “Cauchy” that horizon!
It’s hard they’re fast!
No one can travel into a black hole. There is no way to observe what is happening inside a black hole. So this is just equations. Not observations. The equations cannot be verified against reality.
Glad I’m not a mathematician.
What is “space-time”? Space is a word used for “where there isn’t anything.” Time is the measurement of motion. (Thomas of Aquinas.) Putting them together with a hyphen produces what?
What a coincidence. I was thinking about this just last night.
Glad Im not a mathematician.
I usually retire to my couchy horizon-tal position to watch guys like Michio Kaku on the Science Channel tell me that word like singularity and event horizon are buzz words invented by astrophysicists, when they havent got a clue.
Black Holes are Rasiss.
This is unacceptable. Obviously we need Congress to fund more studies before this gets out of control.
So you can go through and survive!
Warp drive! Time travel!
It is not racist to call something eating that section of the universe near it a black hole. It might however be racist to call someone like Mad Maxine a black hole.
The problem lies in the gap between our ability to describe natural phenomena and the actual reality of the phenomena.
Plus, in astrophysics, it is impossible to observe just about anything directly. Thus, mathematical equations are used to approximate the observable physical reality and extrapolate the unobservable from that.
This is why I am not a theoretical physicist. I prefer a scientific discipline in which I can make predictions and conduct the experiments that show whether they are accurate or not. I don’t have to extrapolate from a handful of observations to make predictions about things which are forever unobservable. I deal with predictable physics. Well, predictable until one gets down to the quantum level...even there, the outcomes are predictable.
If I only had a dollar for every time I've said that.
Phil Spector said he wished he had a nickel for every joint Brian Wilson smoked trying to figure out how Spector got the "Be My Baby" sound.
Never heard it explained as well as that, thanks!
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