*why*it’s wrong. Sure, some are easy, but those are mostly the ones people send me via email trying to get me to buy their ebook containing the Theory of Everything. The tough ones are the ones that get published, or are by professional scientists who bypass peer review and go directly to the press release.

That’s the case of a paper released this week. The authors — a pair of physicists working in the US and Canada — claim they have strongly demonstrated that black holes can never form, and so they don’t exist. Never mind that we see astronomical objects that are too compact and massive for neutron stars — the authors don’t even consider that problem. Instead, they look at the problem of gravitational collapse into a black hole, including the effect of Hawking radiation: the particles emitted due to quantum effects in strong gravity. The authors found that the amount of Hawking radiation prevented the star from forming an event horizon, resulting in no black hole. (Some people might be confused at this point: how can there be Hawking radiation before there’s a black hole? The answer is a little esoteric, so I’ll answer it in the next section.) Here’s what I said in *The Daily Beast*:

Most calculations of massive stars collapsing into black holes use general relativity, Einstein’s theory of gravitation, which doesn’t include any quantum effects. In the new paper, the authors claim that if you include Hawking radiation, the emission of particles from a black hole’s surface, the extra contribution is enough to stop gravitational collapse and prevent a black hole from forming. I’ll say straight out: I think these results are wrong. However, seeing why is important, and part of the process of science. [read more…]

Unlike the majority of the “black holes don’t exist OMG!!!” papers that cross my desk, this one isn’t obviously wrong. As gravitational researchers, the authors know what they’re doing, so any problem with the calculation can’t just be spotted outright. I spent all day Thursday on the paper (a task complicated by the fact that I haven’t seriously worked on stuff like this in about 10 years), and I’m not so arrogant to believe I’ve definitely found the problem. However, I’m heartened by the fact that legit gravitational physicist Sabine Hossenfelder also dug into the paper, and draws similar conclusions to mine. (In fact, if I were smart, I’d just let you all go read what she says, but I still want to make sure *I* understand, and the best way to do that is to write it all out.)

### Collapse into now

The authors model the collapse of a star as best as possible from first principles using a set of straightforward equations from general relativity, which they then solve with a computer. The key part of the calculation is the energy transfer between the particles of the collapsing star and the Hawking radiation. (For those keeping track at home, they model Hawking radiation classically, treating it as just another energy source; more on this in the next section.) That transfer of energy stops the collapse of the star and reverses it, at which point the computer solution breaks down, so they can’t answer the question of what forms instead of a black hole.

From what I can tell, the authors get a *lot* more Hawking radiation than is typical, which contradicts earlier work from the 1970s on. While I suppose they could be finding something others have missed, their modeling is straightforward enough that I suspect not: if black holes really can’t form, then something subtle and perhaps fundamentally new must be going on.

And honestly, the paper probably wouldn’t draw this much scrutiny — and I certainly wouldn’t be spending this much time on it — if the university where the lead author works hadn’t sent out a press release claiming the calculation definitely shows black holes don’t exist. That’s an amazingly strong claim to make, not least since the paper hasn’t even passed peer review for publication in a journal yet. (That’s not a perfect criterion, of course, and more people are able to peer-review the paper pre-publication thanks to its free availability on the ArXiv.)

### Rage, rage against the dying of the light

A black hole is an object with an *event horizon*, a boundary beyond which no object can return to the outside once it crosses. According to general relativity, a sufficiently high concentration of mass will collapse under its own gravity, until an event horizon forms. Once that happens, any matter inside will continue to collapse; since it can’t recross the event horizon, it’s trapped forever. And of course, once you’ve got a black hole, further gravitational collapse will only make it grow. So, if you want to stop a black hole, you have to prevent the event horizon from forming in the first place.

One possible out involves Hawking radiation. Usually we focus on the Hawking radiation produced by an event horizon, when (in the simplest version) pairs of particles are produced via the rules of quantum field theory by the intense gravity. One of that pair falls in, while the other escapes; the effect is to reduce the mass of the black hole very slightly. However, that’s a simplification good enough for most discussions, and we need to go past that now.

Quantum field theory predicts predicts particles being produced during gravitational collapse as well. If we observe a black hole from far away (please, let’s observe black holes from far away), we never see the endpoint of collapse, only a slowing down as particles approach the event horizon. In that sense, the event horizon is always in our future, and gravitational collapse goes on literally forever. That may sound like I’m saying black holes don’t exist, but that’s because we are observing from a distance. If we were to fall into a black hole ourselves, or ride the collapsing star into oblivion like some suicidal sci-fi hero, we would definitely see the event horizon form, and once we passed it, we would never be able to return to the outside Universe.

For the present discussion, that means Hawking radiation is emitted during gravitational collapse because in a sense we’re *always* observing collapse. Therefore, *if* enough energy was carried away by the radiation, it could prevent an event horizon from forming. Researchers considered that idea as early as the 1970s, with others resurrecting it at irregular intervals since. So the new paper isn’t a new idea, but it may be a new approach to that idea, using computer modeling to get a solution to the exact equations from general relativity. (I haven’t done a thorough literature review, but I trust the authors of the paper did. If they’re like me, they’re paranoid that someone else already did the same calculation.)

So the real question is whether they went about calculating the amount of Hawking radiation properly, and understanding why they got a result at odds with what other researchers have obtained. (Anyone uninterested, please feel free to skip this paragraph.) On this front — and I may be entirely wrong! — I think they do two things that lead to a larger-than-usual estimate of Hawking radiation. First, *all* the radiation seems to be emitted from a single radius, when the density of the radiation produced should change. Second, if I understand the equations, I *think* all the energy produced by the Hawking radiation in their model is transferred to the collapsing matter, when the actual transfer would be far less efficient. [**Update: **I’m probably wrong on the energy transfer; see Ian Hawke’s comment below.] Again, I may be wrong on these points, so don’t take this paragraph as a peer-review-worthy analysis of the paper; Sabine Hossenfelder points out that they may be also overestimating the energy from the Hawking particles because they treat the shell of collapsing matter like the event horizon for the sake of calculating the energy radiated away.

But whether my thinking is right or wrong, the point is that we can — and should! — check the results before declaring black holes dead. When a new paper is strongly at odds with other calculations, the first response shouldn’t be to rush to press and shout about how everything has changed. That’s *especially* true when some aspects of the work are still preliminary; science is often a process of refinement as much as it is one of discovery. If anything, the more radical the result, the more skepticism it should face; I expect black holes will survive to another day.

I *think* you’re wrong about the second point (energy transferred to the collapsing matter). I think their presentation of this is confused as well, as they talk about energy transfer between the “star” and the “Hawking radiation”.

What I think they’ve got is two matter sources; the “star” (a dust fluid) and the Hawking radiation (a null dust fluid). Both are minimally coupled to gravity, and couple to each other only indirectly via the spacetime. The equations of motion of the star are the standard conservation of stress-energy, which involves derivatives of the Hawking radiation. The Hawking radiation is provided by the (seemingly dodgy) ansatz, closing the system.

I interpret this as: energy transferred from spacetime to Hawking radiation, which “propagates out” (positive energy out and negative energy in), which effectively reduces the gravitational potential (or redistributes in further away from the origin), slowing the collapse of the fluid.

There’s some ways in which this is related to the “spontaneous scalarization” simulations of Barausse and Palenzuela (eg http://journals.aps.org/prd/abstract/10.1103/PhysRevD.89.044024). In the scalar-tensor model they’re using the ansatz leads to similar equations and some odd behaviour, but isn’t such an… emotive issue.

That would make a lot more sense than my reading, but yeah: they do make it sound in the text like there’s direct transfer. And just to be plain, I’m willing to be wrong on this!

One good thing about begging for publicity, though: someone will likely do a more detailed recalculation than I have time or resources to do.

Mr.Ian Hawke

Maybe you will explain to me,whence in the finite universe or in finite space [ Black Hole ] infinite gravity force ?,finite space can only have a finite force and similarly infinite force needs infinite space,as with our universe is finite-standard model and Big Bang,from where you took infinite force ?

I’m not that good with blackhole theory.My question might seem silly,i’ll ask it anyway-:

Why isn’t the inward pressure of the particles(created as a result of QFT) considered?If there are inward bound particles moving towards the centre of mass of the star,resulting in net pressure contribution (due to QFT particles) becoming zero?

The full answer to your question is too complicated for a quick response, unfortunately. However, you can think of it this way: gravitational collapse is what

createsthe Hawking radiation particles in the first place. Energy is being extracted from the inner part of the collapsing region and moved into the outer part; see Sabine Hassenfelder’s blog post for more details on that.