It is one of my most-favorite figures in a physics paper. I'm still bummed that PRL made them remove it in the final version.

What, really? Why? It's one of my go-to examples of clear, impactful data presentation.

More precisely, a black hole five times as massive as the Earth. And it fits on a page. I think I have to print that out and pin it to a wall somewhere...

At what range would the gravity differential kill you? Would you be able to see it before it kills you? If it was close to the sun we should be seeing some kind of halo around it due to gravitational lensing right?

edit: ok maybe we'd need it to be between us and the sun for that to work, the lensing would be that of other stars I guess. I suppose the important question is, since it's relatively close to us, would it deform space hard enough for the gravitational lensing to be noticeable at such close proximity.

edit2: more train of thought, just because it's fun, I suppose since it's so small and the gravity relatively weak (i.e. not as strong as some huge stars or galaxies) any halo or distortion would not extend more than a couple meter, which wouldn't be noticeable from our distance, right?

As usual the answer is - it depends, but we could estimate forces in question. Assuming my math is correct, at 67 kilometers getting 1 meter closer will results in gravitational pull difference of 137kg. At 40 kilometers, this number increases to ~623kg. I am assuming bad things will happen somewhere between those two ranges.

F = G * (m1 * m2) / r^2 . G = 6.674 / 10^11 (m^3 / (kg * s^2)) | m1 = 5 * 5.972 * 10^24 kg | m2 = 100 kg

Only r in the equation above is not a constant, so we can compute F(r) - F(r+1) to get a difference in force that being 1 meter closer to the black hole would make at a distance r. Basically, this is the difference between how hard your toes would be pulled down vs your heard if you curl into a ball.

  Distance Force          Force + 1      Diff in kg
  1        1.99286E+17    4.98214E+16    1.49464E+16
  1000     1.99286E+11    1.98888E+11    39797421.92
  10000    1992856400     1992457888     39851.15023
  20000    498214100      498164282.3    4981.767364
  30000    221428488.9    221413727.7    1476.11612
  40000    124553525      124547297.6    622.744272
  50000    79714256       79711067.53    318.8474585
  60000    55357122.22    55355277.03    184.5191277
  70000    40670538.78    40669376.79    116.1990494

Very cool, thanks! It's closer than I thought, yet just too far to see it unless it's causing things to happen around it. I suppose if it would crash (slowly :p) into the earth and you were at 67 kilometers you'd see some crazy things.

Worth remember for comparison that the Kármán line is at 100 kilometers. ISS orbits at ~400 kilometers. So, if such a hole were to appear on the surface of the planet, even the crew of the ISS would have a very bad day.

Well the ISS orbits at R_earth + 400 km. So it wouldn't be nearly as bad as that number makes it sound.

Before you got very far into this it would be really hard to stay curled up in a ball.

Does anyone know how fast one would fall in from a 100km initial distance?

This answer: https://physics.stackexchange.com/a/332510/236187 seems to suggest that it takes mere milliseconds once one is within three times the Schwarzschild radius of the black hole. And that dozens of radii outward, one already moves at a significant fraction of the speed of light.

I believe that the Roche limit would be roughly the same as it is on earth. However, the gravity constant would be the same. So for something as massive as a person, you should not experience any destructive forces until you reached extremely close to the object. Probably measured in a handful of miles or less.

Einstein: "Time and space are not conditions in which we live, but modes by which we think. Physical concepts are free creations of the human mind, and are not, however it may seem, determined by the external world."

Paul Brunton: "The most valuable metaphysical fruit of the quantum theory is its finding that the processes of the universe which occur in space and time, emanate from what is fundamentally not in space and time."

Nisargadatta Maharaj: "In reality, time and space exist in you. You do not exist in them."

And furthermore, "God does not play dice with the universe."

So basically, Kant called it

Kind of cute. Immediately reminded me of this (for you Beatles fans out there).

http://www.westfieldcomics.com/blog/wp-content/uploads/2018/...

I used to read that to my daughter and make all the voices from the movie.

It's a great kids' book.

Go lasso that horse and ride it to the stars!

https://en.wikipedia.org/wiki/Black_hole_starship

Halo Drive: Fire a laser around the Halo and get more energy reflected back than you put in.

https://www.youtube.com/watch?v=rFqL9CkNxXw&t=2s

> FIG. 1. Exact scale (1:1) illustration of a 5M⊕ PBH. Note that a 10M⊕ PBH is roughly the size of a ten pin bowling ball.

And it's oddly terrifying.

One of these things intersecting with Earth would be an interesting way for humanity to end.

The real question is, with the warping of space-time, how long would it take for us to perceive the end? Would it seem like the black hole started moving incredibly slowly, or would our planet start getting torn apart before then?

This is the premise of a book by Thomas Wren:

https://www.goodreads.com/book/show/2335064.The_Doomsday_Eff...

From (distant) memory it was a fun read with some science but not overly realistic wrt to how humanity would react.

A very large black hole would have a hard time sneaking up on me, but one the size of a bowling ball on the other hand...

Nibbler would be proud.

Wouldn't there be life-ending amounts of Hawking radiation coming from it? In other words, not a black circle :-)

From the PDF:

> On its own, a PBH of mass 5M⊕ has a Hawking temperature of 0.004 K, making it colder than the CMB, and since it’s radius is rBH ∼ 5 cm, the power radiated by the PBH alone is minuscule.

Also wolfram alpha says it would take 7e52 years to evaporate from hawking radiation, so it's quite stable: https://www.wolframalpha.com/input/?i=%285120*pi*G%5E2*%285+...

My understanding is that a black hole large enough to be colder than the CMB will grow (gain more mass energy by absorbing CMB photons, even in "empty" space, than it loses by Hawking radiation), continuing to cool.

I assume but am not sure that the cooling of an already-sufficiently-cold black hole in this manner is slower than the cooling of the CMB itself due to expansion, so that at some point as the universe winds down it will begin to shrink again and eventually evaporate, but definitely over the lifetime of any star we see a black hole this side won't radiate significantly, or evaporate.

I did the figures a while back on what it would take to build a Hawking-radiation-basedv mass-to-energy power plant (in orbit, obviously), and I was astounded at how tiny the black holes have to be in order to get appreciable power output from them.

I can resize pdfs...

How far from this black hole would the event horizon be?

In the current theory of GR (which predicts the existence of black holes), black holes themselves are point singularities - so the only meaning for "size" is the event horizon.

Note that physicists don't believe this 0-size point is actually correct - the expectation is that a theory of quantum gravity would predict some fixed size for the black hole, one that also prevents the infinities inherent in the GR description of black holes.

Not quite. Point singularities can't spin, and since a black hole with no spin as about as possible as real mass with a temperature of absolute zero, every black hole we're ever likely to observe is actually a ringularity or other two-dimensional configuration.

Thanks for this comment, it was enlightening. I'd never much thought about this because physics is really not my forte, but after a few minutes of thinking about it, it's really intuitive why a point singularity can't spin. I can't explain it in any properly rigorous or technical way, but it makes no sense that someone could (by convention, of course) designate a "front" and "rear" to a mass with zero length in every direction.

What does it mean “to spin” in this case?

It means the black hole has angular momentum, which is detectable due to the resultant frame dragging (effect of the spinning on the spacetime around it) and presumably also due to the flattening of the sphere of the event horizon.

As I understand it, the fact that black holes are rotating precludes them from actually being a point singularity -- "rotation" having no meaning for a non-dimensional point. So they need to have some kind of disk or ring structure (still infinitely thin, however). (Note: I'm not a physicist, could be completely wrong).

That is the event horizon: when discussing a black hole's "size", you're discussing the event horizon.

Worth noting: despite the fact that this black hole would have an event horizon 4.5 cm in diameter, that doesn't mean you could get anywhere near it or put it in a box or anything.

I want to touch it.

and when you close to it it's almost impossible to resist.

"when you stare into the abyss..."

I'd rather hit it with a baseball bat, personally...

rip my ink cartridge trying to print that out

It would be a funny hack to try to trick a printer with malformed content to over-print that section of paper a multitude of times.

This is absolutely something you can do with ASCII dot-matrix printers, and it's not even malformed! It was common to end a line with a CR rather than a CRLF in order to overstrike some characters three times for bold, or overstrike them with _ for underlining; somewhat less common was to overstrike several different characters to get a solid block (such as 0, #, and *). (Accented characters were likewise achieved by overstriking `, ', and ~, but usually using backspace rather than CR.) With a normal amount of ink on the ribbon, you would punch through the paper after less than ten overstrikes.

I understand that line printers (those that printed a line at a time rather than a character at a time) also supported overstrike sequences, but I never punched through the paper on one. Likewise, presumably the same approach would work with a daisy-wheel or typeball printer, but I can't testify.

So small, can I make a ball peen hammer out of it and be the... lesser Thor?

If you can lift it, er... before it absorbs you, then you must already have supernatural powers, so you can join the Norse gods.

And absorbed by black hole would pretty memorable at my memorial. Its win-win.

Probably the only way to die that would also result in you outliving everyone you ever knew.

Unless they followed you