Category: Physics: Black Holes and Relativity

SPLASH Splish plink

On By rolcottIn Astronomy: Stellar Science, Physics: Black Holes and Relativity, UncategorizedLeave a comment

<chirp, chirp, chirp, chirp> “Moire here. This’d better be good.”

“Hello, Mr Moire. I’m one of your readers.”

“Do you have any idea what time it is?”

“Afraid not, I don’t know what time zone you’re in.”

“It’s three o’clock in the morning! Why are you calling me at this hour?”

“Oh, sorry, it’s mid-afternoon here. Modern communications tech is such a marvel. No matter, you’re awake so here’s my question. I’ve been pondering that micro black hole you’ve featured in the last couple of posts. You convinced me it would have a hard time hitting Earth but then I started thinking about it hitting the Sun. The Sun’s diameter is 100 times Earth’s so it presents 10,000 times more target area, yes? Further, the Sun’s 300,000 times more massive than Earth so it has that much more gravity. Surely the Sun is a more effective black hole attractor than Earth is.”

“That’s a statement, not a question. Worse yet, you’re comparing negligible to extremely negligible and neither one is worth losing sleep over which is what I’m doing now.”

“Wait on, I’ve not gotten to my question yet which is, suppose a black hole did happen to collide with the Sun. What would happen then?”

<yawn> “Depends on the size of the black hole. If it’s supermassive, up in the billion‑sun range, it wouldn’t hit the Sun. Instead, the Sun would hit the black hole but there’d be no collision. The Sun would just sink quietly through the Event Horizon.”

“Wouldn’t it rip apart?”

“You’re thinking of those artistic paintings showing great blobs of material being torn away by a black hole’s gravity. Doesn’t work that way, at least not at this size range.” <grabbing Old Reliable from my nightstand and key‑tapping> “Gravitational forces are distance‑dependent. Supermassives are large even by astronomical standards. The M87* black hole, the first one ESA got an image of, has the mass of 6 billion Suns and an Event Horizon three times wider than Pluto’s orbit. The tidal ripping‑apart you’re looking for only happens when the mass centers of two objects approach within Roche’s limit. Suppose a Sun‑sized star flew into M87*’s Event Horizon. Their Roche limit would be 100 astronomical units inside the Event Horizon. If any ripping happened, no evidence could escape to us.”

“Another illusion punctured.”

“Don’t give up hope. The next‑smaller size category have masses near our Sun’s. The Event Horizon of a 10‑solar‑mass black hole would be only about 60 kilometers wide. The Roche Zone for an approaching Sun is a million times wider. There’s plenty of opportunity for ferocious ripping on the way in.”

“Somehow that’s a comfort, but my question was about even smaller black holes — micro‑size flyspecks such as you wrote about. What effect would one have on the Sun?”

“You’d think it’d be a simple matter of the micro‑hole, let’s call it Mikey, diving straight to the Sun’s center while gobbling Sun‑stuff in a gluttonous frenzy, getting exponentially bigger and more voracious every second until the Sun implodes. Almost none of that would happen. The Sun’s an incredibly violent place. On initial approach Mikey’d be met with powerful, rapidly moving magnetic fields. If he’s carrying any charge at all they’d give him whip‑crack rides all around the Sun’s mostly‑vacuum outer layers. He might not ever escape down to the Convection Zone.”

“He’d dive if he escaped there or he’s electrically neutral.”

“Mostly not. The Convection Zone’s 200,000-kilometer depth takes up two‑thirds of the Sun’s volume and features hyper‑hurricane winds roaring upward, downward and occasionally sideward. Mikey would be a very small boat in a very big forever storm.”

“But surely Mikey’s density would carry him through to the core.”

“Nope, the deeper you go, the smaller the influence of gravity. Newton proved that inside a massive spherical shell, the net gravitational pull on any small object is zero. At the Sun’s core it’s all pressure, no gravity.”

“Then the pressure will force‑feed mass into Mikey.”

“Not so much. Mikey has jets and and an accretion disk. Their outward radiation pressure sets an upper limit on Mikey’s gobbling speed. The Sun will nova naturally before Mikey has any effect.”

“No worries then.”

~~ Rich Olcott

Hiding Among The Hill Spheres

On By rolcottIn Astronomy, Physics: Black Holes and Relativity, Space Travel, UncategorizedLeave a comment

Bright Spring sunlight wakes me earlier than I’d like. I get to the office before I need to, but there’s Jeremy waiting at the door. “Morning, Jeremy. What gets you here so soon after dawn?”

“Good morning, Mr Moire. I didn’t sleep well last night, still thinking about that micro black hole. Okay, I know now that terrorists or military or corporate types couldn’t bring it near Earth, but maybe it comes by itself. What if it’s one of those asteroids with a weird orbit that intersects Earth’s orbit? Could we even see it coming? Aren’t we still in danger of all those tides and quakes and maybe it’d hollow out the Earth? How would the planetary defense people handle it?”

“For so early in the day you’re in fine form, Jeremy. Let’s take your barrage one topic at a time, starting with the bad news. We know this particular object would radiate very weakly and in the far infrared, which is already a challenge to detect. It’s only two micrometers wide. If it were to cross the Moon’s orbit, its image then would be about a nanoarcsecond across. Our astrometers are proud to resolve two white‑light images a few milliarcseconds apart using a 30‑meter telescope. Resolution in the far‑IR would be about 200 times worse. So, we couldn’t see it at a useful distance. But the bad news gets worse.”

“How could it get worse?”

“Suppose we could detect the beast. What would we do about it? Planetary defense people have proposed lots of strategies against a marauding asteroid — catch it in a big net, pilot it away with rocket engines mounted on the surface, even blast it with A‑bombs or H‑bombs. Black holes aren’t solid so none of those would work. The DART mission tried using kinetic energy, whacking an asteroid’s moonlet to divert the moonlet‑asteroid system. It worked better than anyone expected it to, but only because the moonlet was a rubble pile that broke up easily. The material it threw away acted as reaction mass for a poorly controlled rubble rocket. Black holes don’t break up.”

“You’re not making getting to sleep any easier for me.”

“Understood. Here’s the good news — the odds of us encountering anything like that are gazillions‑to‑one against. Consider the probabilities. If your beast exists I don’t think it would be an asteroid or even from the Kuiper Belt. Something as exotic as a primordial black hole or a mostly‑evaporated stellar black hole couldn’t have been part of the Solar System’s initial dust cloud, therefore it wouldn’t have been gathered into the Solar System’s ecliptic plane. It could have been part of the Oort cloud debris or maybe even flown in on a hyperbolic orbit from far, far away like ‘Oumuamua did. Its orbit could be along any of an infinite number of orientations away from Earth’s orbit. But it gets better.”

“I’ll take all the improvement you can give me.”

“Its orbital period is probably thousands of years long or never.”

“What difference does that make?”

“You’ve got to be in the right place at the right time to collide. Earth is 4.5 billion years old. Something with a 100‑year orbit would have had millions of chances to pass through a spot we happen to occupy. An outsider like ‘Oumuamua would have only one. We can even figure odds on that. It’s like a horseshoe game where close enough is good enough. The object doesn’t have to hit Earth right off, it only has to pierce our Hill Sphere.”

“Hill Sphere?”

“A Hill Sphere is a mathematical abstract like an Event Horizon. Inside a planet’s Sphere any nearby object feels a greater attraction to the planet than to its star. Velocities permitting, a collision may ensue. The Sphere’s radius depends only on the average planet–star distance and the planet and star masses. Earth’s Hill Sphere radius is 1.5 million kilometers. Visualize Hill Spheres crowded all along Earth’s orbit. If the interloper traverses any Sphere other than the one we’re in, we survive. It has 1 chance out of 471 . Multiply 471 by 100 spheres sunward and an infinity outward. We’ve got a guaranteed win.”

“I’ll sleep better tonight.”

~~ Rich Olcott

A Tug at The Ol’ Gravity Strings

On By rolcottIn Physics: Black Holes and Relativity, Space Travel, UncategorizedLeave a comment

“Why, Jeremy, you’ve got such a stunned look on your face. What happened? Is there anything I can do to help?”

“Sorry, Mr Moire. I guess I’ve been thinking too much about this science fiction story I just read. Which gelato can I scoop for you?”

“Two dips of mint, in a cup. Eddie went heavy with the garlic on my pizza this evening. What got to you in the story?”

“The central plot device. Here’s your gelato. In the story, someone locates a rogue black hole hiding in the asteroid belt. Tiny, maybe a few thousandths of a millimeter across, but awful heavy. A military‑industrial combine uses a space tug to tow it to Earth orbit for some kind of energy source, but their magnetic grapple slips and the thing falls to Earth. Except it doesn’t just fall to Earth, it’s so small it falls into Earth and now it’s orbiting inside, eating away the core until everything crumbles in. I can’t stop thinking about that.”

“Sounds pretty bad, but it might help if we run the numbers.” <drawing Old Reliable from its holster> “First thing — Everything about a black hole depends on its mass, so just how massive is this one?” <tapping on Old Reliable’s screen with gelato spoon> “For round numbers let’s say its diameter is 0.002 millimeter. The Schwartzschild ‘radius’ r is half that. Solve Schwartschild’s r=2GM/c² equation for the mass … plug in that r‑value … mass is 6.7×1020 kilograms. That’s about 1% of the Moon’s mass. Heavy indeed. How did they find this object?”

“The story didn’t say. Probably some asteroid miner stumbled on it.”

“Darn lucky stumble, something only a few microns across. Not likely to transit the Sun or block light from any stars unless you’re right on top of it. Radiation from its accretion disk? Depends on the history — there’s a lot of open space in the asteroid belt but just maybe the beast encountered enough dust to form one. Probably not, though. Wait, how about Hawking radiation?”

“Oh, right, Stephen Hawking’s quantum magic trick that lets a black hole radiate light from just outside its Event Horizon. Does Old Reliable have the formulas for that?”

“Sure. From Hawking’s work we know the object’s temperature and that gives us its blackbody spectrum, then we’ve got the Bekenstein‑Hawking equation for the power it radiates. Mind you, the spectrum will be red‑shifted to some extent because those photons have to crawl out of a gravity well, but this’ll give us a first cut.” <more tapping> “Chilly. 170 kelvins, that’s 100⁰C below room temperature. Most of its sub‑nanowatt emission will be at far infrared wavelengths. A terrible beacon. But suppose someone did find this thing. I wonder what’ll it take to move it here.”

“Can you calculate that?”

“Roughly. Suppose your space tug follows the cheapest possible flight path from somewhere near Ceres. Assuming the tug itself has negligible mass … ” <more tapping> “Whoa! That is literally an astronomical amount of delta-V. Not anything a rocket could do. Never mind. But where were they planning to put the object? What level orbit?”

“Well, it’s intended to beam power down to Earth. Ions in the Van Allen Belts would soak up a lot of the energy unless they station it below the Belts. Say 250 miles up along with the ISS.”

“Hoo boy! A thousand times closer than the Moon. Force is inverse to distance squared, remember. Wait, that’s distance to the center and Earth’s radius is about 4000 miles so the 250 miles is on top of that. 250,000 divided by 4250 … quotient squared … is a distance factor of almost 3500. Put 1% of the Moon that close to the Earth and you’ve got ocean tides 36 times stronger than lunar tides. Land does tides, too, so there’d be earthquakes. Um. The ISS is on a 90‑minute orbit so you’d have those quakes and ocean tides sixteen times a day. I wouldn’t worry about the black hole hollowing out the Earth, the tidal effect alone would do a great job of messing us up.”

“The whole project is such a bad idea that no-one would or could do it. I feel better now.”

~~ Rich Olcott

Science or Not-science?

On By rolcottIn General, Physics: Black Holes and Relativity, UncategorizedLeave a comment

Vinnie trundles up to Jeremy’s gelato stand. “I’ll take a Neapolitan, one each chocolate, vanilla and strawberry.”

“Umm… Eddie forgot to order more three-dip cones and I’m all out. I can give you three separate cones or a dish.”

“The dish’ll be fine, way less messy. Hey, Sy, I got a new theory.”

“Mm… Unless you’ve got a lot of firm evidence it can’t be a theory. Could be a conjecture or if it’s really good maybe a hypothesis. What’s your idea?”

“Thing is, Sy, there can’t be any evidence. Ever. That’s the fun of it.”

“Conjecture, then. C’mon, out with it.”

“Well, you remember all that stuff about how time bends toward a black hole’s mass and that’s how gravity works?”

“Sure, except it’s not just black holes. Time bends the same way toward every mass, it’s just more intense with black holes.”

“Understood. Anyway, we talked once about how stars collapse to form black holes but that’s only up to a certain size, I forget what—”

“Ten to fifteen solar masses. Beyond that the collapse goes supernova and doesn’t leave much behind but dust.”

“Right. So you said we don’t know how to make size‑30 black holes like the first pair that LIGO found.”

“We’ve got a slew of hypotheses but the jury’s still out.”

“That’s what I hear. Well, if we don’t even know that much then we for‑sure don’t know how to make the supermassive black hole the science magazines say we’ve got in the middle of the Milky Way.”

“We’ve found that nearly every galaxy has one, some a lot bigger than ours. Why that’s true is one of the biggest mysteries in astrophysics.”

“And I know the answer! What if those supermassive guys started out as just big lumps of dark matter and then they wrapped themselves in more dark matter and everything else?”

“Cute idea, but the astronomy data says we can account for galaxy shapes and behavior if they’re embedded at the center of a spherical halo of dark matter.”

“Not a problem, Sy. Look at the numbers. Our superguy is a size‑4‑million, right? The whole Milky Way’s a billion times heavier than that. Tuck an extra billionth into the middle of the swirl and the stars wouldn’t see the difference.”

“Okay, but there’s more data that says dark matter spreads itself pretty evenly, doesn’t seem to clump up like you need it to.”

“Yeah, but maybe there’s two kinds, one kind clumpy and the other kind not. Only way to find out is to look inside a superguy but time blocks information flow out of there. So no‑one can say I’m wrong!”

“But sir, that’s not science!”

“Why not, kid?”

“The unit my philosophy class did on Popper.”

“The stuff you sniff or the penguins guy?”

“Neither, Karl Popper the philosopher. Dr Crom really likes Popper’s work so we spent a lot of time reading him. Popper was one of the Austrian intellectuals the Nazis chased out when they took power in the 1930s. Popper traveled around, wound up in New Zealand where he wrote his Open Society book that shredded Hegel and Marx. Those sections were fun reading even if they were wordy. Anyway, one of Popper’s big things was the demarcation problem, how to tell the difference between what’s a scientific assertion and what’s not. He decided the best criterion was if there’s a way to prove the assertion false. Not whether it was false but whether it could at least be tested. I was surprised by how many goofy things the Greeks said that would qualify as Popper‑scientific even though they were just made up and have been proven wrong.”

“Well there you go, Vinnie. Physics and the Universe don’t let us see into a supermassive black hole, therefore your idea isn’t testable even in principle. Jeremy’s right, it’s not scientific even though it’s all dressed up in a Science suit.”

“I can still call it a conjecture, though, right, Sy?”

“Conjecture it is. Might even be true, but we’ll never know unless we somehow find out something about dark matter that surprises us. We’ve been surprised a lot, though, so don’t give up hope.”

~~ Rich Olcott

Imagine A Skyrocket Inside A Black Hole

On By rolcottIn Cosmology, Physics: Black Holes and Relativity, UncategorizedLeave a comment

Vinnie’s never been a patient man. “We’re still waiting, Sy. What’s the time-cause-effect thing got to do with black holes and information?”

“You’ve got most of the pieces, Vinnie. Put ’em together yourself.”

“Geez, I gotta think? Lessee, what do I know about black holes? Way down inside there’s a huge mass in a teeny singularity space. Gravity’s so intense that relativity theory and quantum mechanics both give up. That can’t be it. Maybe the disk and jets? No, ’cause some holes don’t have them, I think. Gotta be the Event Horizon which is where stuff can’t get out from. How’m I doing, Sy?”

“You’re on the right track. Keep going.”

“Okay, so we just talked about how mass scrambles spacetime, tilts the time axis down to point towards where mass is so axes stop being perpendicular and if you’re near a mass then time moves you even closer to it unless you push away and that’s how gravity works. That’s part of it, right?”

“As rain. So mass and gravity affect time, then what?”

“Ah, Einstein said that cause‑and‑effect runs parallel with time ’cause you can’t have an effect before what caused it. You’re saying that if gravity tilts time, it’ll tilt cause‑and‑effect?”

“So far as we know.”

“That’s a little weasel-ish.”

“Can’t help it. The time‑directed flow of causality is a basic assumption looking for counter‑examples. No‑one’s come up with a good one, though there’s a huge literature of dubious testimonials. Something called a ‘closed timelike curve‘ shows up in some solutions to Einstein’s equations for extreme conditions like near or inside a black hole. Not a practical concern at our present stage of technology — black holes are out of reach and the solutions depend on weird things like matter with negative mass. So anyhow, what happens to causality where gravity tilts time?”

“I see where you’re going. If time’s tilted toward the singularity inside a black hole, than so is cause‑and‑effect. Nothing in there can cause something to happen outside. Hey, bring up that OVR graphics app on Old Reliable, I’ll draw you a picture.”

“Sure.”

“See, way out in space here this circle’s a frame where time, that’s the red line, is perpendicular to the space dimensions, that’s the black line, but it’s way out in space so there’s no gravity and the black line ain’t pointing anywhere in particular. Red line goes from cause in the middle to effect out beyond somewhere. Then inside the black hole here’s a second frame. Its black line is pointing to where the mass is and time is tilted that way too and nothing’s getting away from there.”

“Great. Now add one more frame right on the border of your black hole. Make the black line still point toward the singularity but make the red line tangent to the circle.”

“Like this?”

“Perfect. Now why’d we put it there?”

“You’re saying that somewhere between cause-effect going wherever and cause-effect only going deeper into the black hole there’s a sweet spot where it doesn’t do either?”

“Exactly, and that somewhere is the Event Horizon. Suppose we’re in a mothership and you’re in our shuttlecraft in normal space. You fire off a skyrocket. Both spacecraft see sparks going in every direction. If you dive below an Event Horizon and fire another skyrocket, in your frame you’d see a normal starburst display. If we could check that from the mothership frame, we’d see all the sparks headed inward but we can’t because they’re all headed inward. All the sparkly effects take place closer in.”

“How about lighting a firework on the Horizon?”

“Good luck with that. Mathematically at least, the boundary is infinitely thin.”

“So bottom line, light’s trapped inside the black hole because time doesn’t let the photons have an effect further outward than they started. Do I have that right?”

“For sure. In fact, you can even think of the hole as an infinite number of concentric shells, each carrying a causality sign reading ‘Abandon hope, all ye who enter here‘. So what’s that say about information?”

“Hah, we’re finally there. Got it. Information can generate effects. If time can trap cause‑effect, then it can trap information, too.”

~~ Rich Olcott

Tilting at Black Holes

On By rolcottIn Physics: Black Holes and Relativity, Physics: Newton and Gravity, UncategorizedLeave a comment

“What’s the cause-effect-time thing got to do with black holes and information?”

“We’re getting there, Al. What happens to spacetime near a black hole?”

“Everybody knows that, Sy, spacetime gets stretched and squeezed until there’s infinite time dilation at the Event Horizon.”

“As usual, Vinnie, what everybody knows isn’t quite what is. Yes, Schwarzschild’s famous solution includes that Event Horizon infinity but it’s an artifact of his coordinate system. Al, you know about coordinate systems?”

“I’m a star-watcher, Sy. Sure, I know about latitude and longitude, declination and right ascension, all that stuff no problem.”

“Good. Well, Einstein wrote his General Relativity equations using generalized coordinates, like x,y,z but with no requirement that they be straight lines or at right angles. Schwarzschild solved the equations for a non‑rotating sphere so naturally he used spherical coordinates — radius, latitude and longitude. Since then other people have solved the equations for more complicated cases using more complicated coordinate systems. Their solutions don’t have that infinity.”

“No infinity?”

“Not that one, anyhow. The singularity at the hole’s geometric center is a real thing, not an artifact. So’s a general Event Horizon, but it’s not quite where Schwarzschild said it should be and it doesn’t have quite the properties that everybody thinks they know it has. It’s still weird, though.”

“How so?”

“First thing you have to understand is that when you get close to a black hole, you don’t feel any different. Except for the spaghettification, of course.”

“It’s frames again, ain’t it?”

“With black holes it’s always frames, Vinnie. If you’re living in a distorted space you won’t notice it. Whirl a meter‑long sword around, you’d always see it as a meter long. A distant observer would see you and everything around you as being distorted right along with your space. They’ll see that sword shrink and grow as it passes through different parts of the distortion.”

“Weird.”

“We’re just getting started, Al. Time’s involved, too. <grabbing a paper napkin and sketching> Here’s three axes, just like x,y,z except one’s time, the G one points along a gravity field, and the third one is perpendicular to the other two. By the way, Al, great idea, getting paper napkins printed like graph paper.”

“My location’s between the Physics and Astronomy buildings, Sy. Gotta consider my clientele. Besides, I got a deal on the shipment. What’s the twirly around that third axis?”

“It’s a reminder that there’s a couple of space dimensions that aren’t in the picture. Now suppose the red ball is a shuttlecraft on an exploration mission. The blue lines are its frame. The thick vertical red line shows it’s not moving because there’s no spatial extent along G. <another paper napkin, more sketching> This second drawing is the mothership’s view from a comfortable distance of the shuttlecraft near a black hole.”

“You’ve got the time axis tilted. What’s that about?”

“Spacetime being distorted by the black hole. You’ve heard Vinnie and me talk about time dilation and space compression like they’re two different phenomena. Thing is, they’re two sides of the same coin. On this graph that shows up as time tilted to mix in with the BH direction.”

“How about those twirly directions?”

“Vinnie, you had to ask. In the simple case where everything’s holding still and you’re not too close to the black hole, those two aren’t much affected. If the big guy’s spinning or if the Event Horizon spans a significant amount of your sky, all four dimensions get stressed. Let’s keep things simple, okay?”

“Fine. So the time axis is tilted, so what?”

“We in the distant mothership see the shuttlecraft moving along pure tilted time. The shuttlecraft doesn’t. The dotted red lines mark its measurements in its blue‑line personal frame. Shuttlecraft clocks run slower than the mothership’s. Worse, it’s falling toward the black hole.”

“Can’t it get away?”

“Al, it’s a shuttlecraft. It can just accelerate to the left.”

“If it’s not too close, Vinnie. The accelerative force it needs is the product of both masses, divided by the distance squared. Sound familiar?”

“That’s Newton’s Law of Gravity. This is how gravity works?”

“General Relativity cut its teeth on describing that tilt.”

~~ Rich Olcott

Cause, Effect And Time

On By rolcottIn Physics: Black Holes and Relativity, Uncategorized2 Comments

We’re still at Vinnie’s table by the door of Al’s coffee shop. “Long as we’re talking about black holes, Sy, I read in one of my astronomy magazines that an Event Horizon traps information the same way it traps light. I understand how gravity makes escape velocity for photons go beyond lightspeed, but how does that trap information?”

“Well, to start with, Al, you understand wrong. The whole idea of escape velocity applies to massive objects like rockets that feel the force of gravity. Going up they trade kinetic energy for potential energy; given enough kinetic energy they escape. Photons have zero mass — the only way gravity influences them is by bending the spacetime they fly through.”

“Does the bending also affect information or is that something else?”

Minkowski’s spacetime diagram…

“Fair question, but it’ll take some background to answer it. Good thing I’ve got Old Reliable and my graphics files along. Let’s start with this one. Vinnie’s seen a lot of spacetime graphs like this, Al, but I don’t think you have. Time runs upward, distance runs sideward, okay? Naming a specific time and location specifies an event, just like a calendar entry. Draw a line between two events; the slope is the speed you have to go to get from one to the other.”

“Just the distance, you’re not worrying about direction?”

“Good question. You’re thinking space is 3D and this picture shows only one space dimension. Einstein’s spacetime equations take account of all four dimensions mixing together, which is one reason they’re so hard to solve except in special cases. For where we’re going, distance will be enough, okay?”

“Not gonna argue.”

… compartmentalized by Einstein’s speed limit …

“Now we roll in Einstein’s speed limit. Relativity says that nothing can go faster than light. On a Minkowski diagram like this we draw the lightspeed slope at a 45″ angle. Any physical motion has a slope more vertical than that.”

“Huh?”

“See, Al, you’re going one second per second along time, right? If you’re not making much progress distance‑wise, you don’t do much on Sy’s sideways axis. You move mostly up.”

“Exactly, Vinnie. The bottom and top sections are called ‘timelike‘ because, well, they’re mostly like time.”

“Are the other two sections spacelike?”

“Absolutely. You can’t get from ‘Here & Now‘ to the ‘Too far to see‘ event without going faster than light. Einstein said that’s a no‑no. Suppose that event’s a nova, ‘Now‘ but far away. Astronomers will have to just wait until the nova’s light reaches them at ‘Here‘ but at a later ‘Now.’ Okay, Vinnie, here’s a graphic you haven’t seen yet.”

… and re-interpreted in terms of causality.

“Looks pretty much the same, except for that arrow. What’s cause and effect got to do with time?”

“I don’t want to get into the metaphysical weeds here. There’s a gazillion theories about time — the Universe is expanding and that drives time; entropy always increases and that drives time; time is an emergent property of the underlying structure of the Universe, whatever that means. From an atomic, molecular, mechanical physics point of view, time is the result of causes driving effects. Causes always come first. Your finger bleeds after you cut it, not before. Cause‑effect runs along the time axis. Einstein showed us that cause‑effect can’t travel any faster than lightspeed.”

“That’s a new one. How’d he figure that?”

“Objects move objects to make things happen. They can’t move faster than lightspeed because of the relativity factor.”

“What if the objects are already touching?”

“Your hand and that cup are both made of atoms and it’s really their electric fields that touch. Shifting fields are limited by lightspeed, too.”

“So you’re saying that cause-effect is timelike.”

“Got it in one. Einstein would say causality is not only timelike, but exactly along the time axis. That’s one big reason he was so uncomfortable about action at a distance — a cause ‘Here‘ having an effect ‘There‘ with zero time elapsed would be a horizontal line, pure spacelike, on Minkowski’s graph. Einstein invented the principle of entanglement as a counterexample, thinking it impossible. He’d probably be shocked and distressed to see that today we have experimental proof of entanglement.”

~~ Rich Olcott

Holes in A Hole?

On By rolcottIn Physics: Black Holes and Relativity, UncategorizedLeave a comment

Mid-afternoon coffee break time so I head over to Al’s coffee shop. Vinnie’s at his usual table by the door, fiddling with some spilled coffee on the table top. I notice he’s pulled some of it into a ring around a central blob. He looks at it for a moment. His mental gears whirl then he looks up at me. “Hey Sy! Can you have a black hole inside another black hole?”

“That’s an interesting question. Quick answer is, ‘No.’ Longer answer is, ‘Sort of, maybe, but not the way you’re thinking.’ You good with that, Vinnie?”

“You know me better than that, Sy. Pull up a chair and give.”

I wave at Al, who brings me a mug of my usual black mud. “Thanks, Al. You heard Vinnie’s question?”

“Everyone on campus did, Sy. Why the wishy-washy?”

“Depends on your definition of black hole.”

Sky-watcher Al is quick with a response. “It’s a star that collapsed denser than a neutron star.”

Vinne knows me and black holes better than that. “It’s someplace where gravity’s so strong that nothing can get out, not even light.”

“Both right, as far as they go, but neither goes deep enough for Vinnie’s question.”

“You got a better one, I suppose?”

“I do, Vinnie. My definitition is that a black hole is a region of spacetime with such intense gravitation that it wraps an Event Horizon around itself. Al’s collapsed star is one way to create one, but that probably doesn’t account for the Event Horizons around supermassive black holes lurking in galactic cores. Your ‘nothing escapes‘ doesn’t say anything about conditions inside.”

“Thought we couldn’t know what happens inside.”

“Mostly correct, which is why your question is as problematical as you knew it was. Best I can do is lay out possibilities, okay? First possibility is that the outer black hole forms around a pre-existing inner one.”

“Can they do that?”

“In principle. What makes a black hole is having enough mass gathered in close proximity. Suppose you have a black hole floating our there in space, call it Fred, and a neutron star comes sidling by. If the two bodies approach closely enough, the total amount of mass could be large enough to generate a second Event Horizon shell enclosing both of them. How long that’d last is another matter.”

“The outer shell’d go away?”

“No chance of that. Once the shell’s created, the mass is in there and the star is doomed … unless the star’s closest approach matches Fred’s ISCO. That’s Innermost Stable Circular Orbit, about three times Fred’s Event Horizon’s half-diameter if Fred’s not rotating. Then the two bodies might go into orbit around their common center of gravity.”

“How’s rotation come into this?”

“If the mass is spinning, then you’ve got a Kerr black hole, frame-dragging and an ISCO each along and against the spin direction. Oh, wait, I forgot about tidal effects.”

“Like spaghettification, right.”

“Like that but it could be worse. Depending on how tightly neutronium holds itself together, which we don’t know, that close approach might be inside the Roche limit. Fred’s gravity gradient might simply shred the star to grow the black hole’s accretion disk.”

“Grim. You said there’s other possibilities?”

“Sorta like the first one, but suppose the total mass comes from two existing black holes, like the collision that LIGO picked up accidentally back in 2014. Suppose each one is aimed just outside the other’s ISCO. Roche fragmentation wouldn’t happen, I think, because each body’s contents are protected inside its own personal Event Horizon. Uhh … darn, that scheme won’t work and neither will the other one.”

“Why not?”
 ”Why not?”

“Because the diameter of an Event Horizon is proportional to the enclosed mass. The outer horizon’s diameter for the case with two black holes would be exactly the sum of the diameters of the embedded holes. If they’re at ISCO distances apart they’re can’t be close enough to form the outer horizon. For the same reason, I don’t think a neutron star could get close enough, either.”

“No hole in a hole, huh?”

“I’m afraid not.”

~~ Rich Olcott

  • Thanks to Alex and Xander, who asked the question.

Maybe It’s Just A Coincidence

On By rolcottIn Physics: Black Holes and Relativity, UncategorizedLeave a comment

Raucous laughter from the back room at Al’s coffee shop, which, remember, is situated on campus between the Physics and Astronomy buildings. It’s Open Mic night and the usual crowd is there. I take a vacant chair which just happens to be next to the one Susan Kim is in. “Oh, hi, Sy. You just missed a good pitch. Amanda told a long, hilarious story about— Oh, here comes Cap’n Mike.”

Mike’s always good for an offbeat theory. “Hey, folks, I got a zinger for you. It’s the weirdest coincidence in Physics. Are you ready?” <cheers from the physicists in the crowd> “Suppose all alone in the Universe there’s a rock and a planet and the rock is falling straight in towards the planet.” <turns to Al’s conveniently‑placed whiteboard> “We got two kinds of energy, right?”

Potential Energy    Kinetic Energy

Nods across the room except for Maybe-an-Art-major and a couple of Jeremy’s groupies. “Right. Potential energy is what you get from just being where you are with things pulling on you like the planet’s gravity pulls on the rock. Kinetic energy is what potential turns into when the pulls start you moving. For you Physics smarties, I’m gonna ignore temperature and magnetism and maybe the rock’s radioactive and like that, awright? So anyway, we know how to calculate each one of these here.”

PE = GMm/R    KE = ½mv²

“Big‑G is Newton’s gravitational constant, big‑M is the planet’s mass, little‑m is the rock’s mass, big‑R is how far apart the things are, and little‑v is how fast the rock’s going. They’re all just numbers and we’re not doing any complicated calculus or relativity stuff, OK? OK, to start with the rock is way far away so big‑R is huge. Big number on the bottom makes PE’s fraction tiny and we can call it zero. At the same time, the rock’s barely moving so little‑v and KE are both zero, close enough. Everybody with me?”

More nods, though a few of the physics students are looking impatient.

“Right, so time passes and the rock dives faster toward the planet Little‑v and kinetic energy get bigger. Where’s the energy coming from? Gotta be potential energy. But big‑R on the bottom gets smaller so the potential energy number gets, wait, bigger. That’s OK because that’s how much potential energy has been converted. What I’m gonna do is write the conversion as an equation.

GMm/R = ½mv²

“So if I tell you how far the rock is from the planet, you can work the equation to tell me how fast it’s going and vice-versa. Lemme show those straight out…”

v = √(2GM/R)    R = 2GM/v²

Some physicist hollers out. “The first one’s escape velocity.”

“Good eye. The energetics are the same going up or coming down, just in the opposite direction. One thing, there’s no little‑m in there, right? The rock could be Jupiter or a photon, same equations apply. Suppose you’re standing on the planet and fire the rock upward. If you give it enough little‑v speed energy to get past potential energy equals zero, then the rock escapes the planet and big‑R can be whatever it feels like. Big‑R and little‑v trade off. Is there a limit?”

A couple of physicists and an astronomy student see where this is going and start to grin.

“Newton physics doesn’t have a speed limit, right? They knew about the speed of light back then but it was just a number, you could go as fast as you wanted to. How about we ask how far the rock is from the planet when it’s going at the speed of light?”

R = 2GM/c²

Suddenly Jeremy pipes up. “Hey that’s the Event Horizon radius. I had that in my black hole term paper.” His groupies go “Oooo.”

“There you go, Jeremy. The same equation for two different objects, from two different theories of gravity, by two different derivations.”

“But it’s not valid for lightspeed.”

“How so?”

“You divided both sides of your conversion equation by little‑m. Photons have zero mass. You can’t divide by zero.”

Everyone in the room goes “Oooo.”

~~ Rich Olcott

A Star’s Tale

On By rolcottIn Astronomy: Stellar Science, Physics: Black Holes and Relativity, UncategorizedLeave a comment

It’s getting nippy outside so Al’s moved his out‑front coffee cart into his shop. Jeremy’s manning the curbside take‑out window but I’m walking so I step inside. Limited seating, of course. “Morning, Al. Here’s my hiking mug, fill ‘er up with high‑test and I’ll take a couple of those scones — one orange, one blueberry. Good news that the Governor let you open up.”

“You know it, Sy. Me and my suppliers have been on the phone every day. Good thing we’ve got long‑term relationships and they’ve been willing to carry me but it gets on my conscience ’cause they’re in a crack, too, ya know?”

“Low velocity of money hurts everybody, Al. Those DC doofuses and their political kabuki … but don’t get me started. Hey, you’ve got a new poster over the cash register.”

“You noticed. Yeah, it’s a beaut. Some artist’s idea of what it’d look like when a star gets spaghettified and eaten by a black hole. See, it’s got jets and a dust dusk and everything.”

“Very nice, except for a few small problems. That’s not spaghettification, the scale is all wrong and that tail-looking thing … no.”

Artist’s impression of AT2019qiz. Credit: ESO/M. Kornmesser
Under Creative Commons Attribution 4.0 International License

“Not spaghettification? That’s what was in the headline.”

“Sloppy word choice. True spaghettification acts on solid objects. Gravity’s force increases rapidly as you approach the gravitational center. Suppose you’re in a kilometer-long star cruiser that’s pointing toward a black hole from three kilometers away. The cruiser’s tail is four kilometers out. Newton’s Law of Gravity says the black hole pulls almost twice as hard on the nose as on the tail. If the overall field is strong enough it’d stretch the cruiser like taffy. Larry Niven wrote about the effect in his short story, Neutron Star.”

“The black hole’s stretching the star, right?”

“Nup, because a star isn’t solid. It’s fluid, basically a gas held together by its own gravity. You can’t pull on a piece of gas to stretch the whole mass. Your news story should have said ‘tidal disruption event‘ but I guess that wouldn’t have fit the headline space. Anyhow, an atom in the star’s atmosphere is subject to three forces — thermal expansion away from any gravitational center, gravitational attraction toward its home star and gravitational attraction toward the black hole. The star breaks up atom by atom when the two bodies get close enough that the black hole’s attraction matches the star’s surface gravity. That’s where the scale problem comes in.”

Al looks around — no waiting customers so he strings me along. “How?”

“The supermassive black hole in the picture, AT2019qiz, masses about a million Suns‑worth. The Sun‑size star can barely hold onto a gas atom at one star‑radius from the star’s center. The black hole can grab that atom from a thousand star‑radii away, about where Saturn is in our Solar System. The artist apparently imagined himself to be past the star and about where Earth is to the Sun, 100 star‑radii further out. Perspective will make the black hole pretty small.”

“But that’s a HUGE black hole!”

“True, mass‑wise, not so much diameter‑wise. Our Sun’s about 864,000 miles wide. If it were to just collapse to a black hole, which it couldn’t, its Event Horizon would be about 4 miles wide. The Event Horizon of a black hole a million times as massive as the Sun would be less than 5 times as wide as the Sun. Throw in the perspective factor and that black circle should be less than half as wide as the star’s circle.”

“What about the comet‑tail?”

“The picture makes you think of a comet escaping outward but really the star’s material is headed inward and it wouldn’t be that pretty. The disruption process is chaotic and exponential. The star’s gravity weakens as it loses mass but the loss is lop‑sided. Down at the star’s core where the nuclear reactions happen the steady burn becomes an irregular pulse. The tail should flare out near the star. The rest should be jagged and lumpy.”

“And when enough gets ripped away…”

“BLOOEY!”

~~ Rich Olcott

  • Thanks to T K Anderson for suggesting this topic.
  • Link to Technical PS — Where Do Those Numbers Come From?.