"Well now," he said. "That answers a theoretical question that I've had on my mind for some time."
I could breathe again, too. "I didn't know what was going to happen there," I said. "I was afraid all the energy might come out of that kernel in one go."
McAndrew nodded. "To be honest, that thought was in my head, too. At this range, the shields would have been useless. We'd have gone like last year's lovers."
Bryson had been watching the whole thing in confusion. We had been ignoring him completely. At last, pale and irritable, he spoke to us again.
"What are you two talking about? And what's happened to the Section with Yifter in it? I was watching on the screen, then it just seemed to disappear."
"McAndrew tried to tell us earlier," I said. "But he didn't want the Lucies to know what he was getting at. He'd been fiddling with the kernel in that Section. You heard what he said—no Killing vector. I don't know what he did, but he fixed it so that the kernel in Section Seven had no Killing vector."
"I'm sure he did," said Bryson tartly. "Now perhaps you'll tell me what a Killing vector is."
"Well, Mac could tell you a lot better than I can. But a Killing vector is a standard sort of thing in relativity—I guess you never had any training in that. You get a Killing vector when a region of space-time has some sort of symmetry—say, about an axis of spin. And every sort of black hole, every sort of kernel we've ever encountered before, has at least one symmetry of that type. So if McAndrew had changed the kernel and made it into something with no Killing vector, it's like no kernel we've ever seen. Right, Mac?"
He looked dreamy. The drugs had taken hold. "I took it past the extreme Kerr-Newman form," he said. "Put it into a different form, metastable equilibrium. Event horizon had disappeared, all the Killing vectors had disappeared."
"Christ!" I hadn't expected that. "No event horizon? Doesn't that mean that you get—?"
McAndrew was still nodding, eye pupils dilated. "—a naked singularity. That's right, Captain. I had a naked singularity, sitting there in equilibrium in Section Seven. You don't get there by spinning-up—needs different method." His speech was slurring, as though his tongue was swollen. "Didn't know what would happen if somebody tried to tap it, to use for a drive. Either the signature of space-time there would change, from three space dimensions and one time, to two space and two time. Or we might see the System's biggest explosion. All the mass coming out as radiation, in one flash."
It was slowly dawning on Bryson what we were saying. "But just where is Yifter now?" he asked.
"Gone a long way," I said. "Right out of this universe."
"And he can't be brought back?" asked Bryson.
"I hope not." I'd seen more than enough of Yifter.
"But I'm supposed to deliver him safely to Titan," said Bryson. "I'm responsible for his safe passage. What am I going to tell the Planetary Coordinators?"
I didn't have too much sympathy. I was too busy looking at McAndrew's wounds. The fingers could be re-generated using the bio-feedback equipment on Titan, but the lung would need watching. It was still bleeding a little.
"Tell them you had a very singular experience," I said. McAndrew grunted as I probed the deep cut in his side. "Sorry, Mac. Have to do it. You know, you've ruined your reputation forever as far as I'm concerned. I thought you were a pacifist? All that preaching at us, then you send Yifter and his lot all the way to Hell—and good riddance to them."
McAndrew was drifting far away on his big dose of painkillers. He half-winked at me and made his curious throat-clearing noise.
"Och, I'm a pacifist all right. We pacifists have to look after each other. How could we ever hope for peace with people like Yifter around to stir up trouble? There's a bunch more of them, a few hours travel behind us. Fix me up quick. I should be tinkering with the other kernels a bit, just in case the other Lucies decide to pay us a visit, later . . ."
Afterword.
When a friend of mine saw the title, "Killing Vector," he said, "I assume that Vector is a person?" I don't know about Vector, but Killing was certainly a person—Wilhelm Killing, a nineteenth century German mathematician after whom Killing fields and Killing vectors are named.
The most frequent complaint I have had about this story is that it is unintelligible. My reply is that it's simply ahead of its time. To my knowledge, it's the only story yet published that provides a description of black holes consistent with present (1979) theories. The modern picture began to emerge in 1974, from Hawking's work at the Institute of Theoretical Astronomy at Cambridge.
Here are a few miscellaneous facts that relate to the story:
Optical scalars (expansion, rotation and shear, as introduced into general relativity by Sachs and Robinson) are affected by the spin of a rotating black hole, as McAndrew said.
It is not possible to "spin up" a Kerr-Newman black hole past a limiting value of the spin—the limit is termed an "extreme" black hole.
Spinors were solidly introduced into general relativity in 1960 by Roger Penrose, who also invented twistors. He may have an Institute named after him when the story takes place, but at the moment he is alive and well, and holds the position of Rouse-Ball Professor of Mathematics at Oxford University.
You can extract energy from a rotating black hole, at least in principle, by passing particles through its ergosphere.
As McAndrew complained, a Schwarzschild black hole, which is uncharged, can't be moved around easily. A charged, spinning black hole (i.e. a kernel) can be moved about with ordinary electromagnetic control. Now all we have to do is find one.
DINSDALE DISSENTS
Yes, what Waldo told you is quite true. He did get an award for his efforts on the Venus terra-forming project, and his medal is genuine. Been boasting again, has he? I'll bet he didn't mention that the President of the United Space Federation opposed the award. Or that it was touch and go whether he got a reward or a life sentence.
No, the President's view had nothing to do with politics. It was a good deal more personal than that.
Let's start at the trial—that's where I got involved. Waldo and I have been friends and partners since law school. I couldn't believe my ears when I heard he'd been arrested for drug smuggling. Taliza's the worst drug on the list, the pusher's dream. Total addiction after one snort. And Waldo disapproves even of tobacco. It was so out of character that I was sure he must be innocent.
The drug ring had been extracting pure taliza from the plants, then putting it into metal powder compacts and shipping them all over Earth. Waldo had handled all the shipping and customs details. He made no attempt to deny it. He said he'd been approached, out of the blue, by a group who wanted to use his experience in international work. That seemed reasonable, because he'd worked for years in the international market. But there were snags.
"You say you believed," said the prosecuting counsel, "that somebody would pay you ten thousand credits a month, just to make shipping arrangements for a lot of cheap brass compacts? Isn't that much higher than your usual rates, Mr. Burmeister?"
Waldo hummed and hawed. He didn't have a good answer. If you ask me, he had suspected from the start that something shady was going on. I think he may even have guessed at smuggling—but gold, not drugs. As I say, Waldo has certain standards of honor.
I became increasingly uneasy as the prosecutor kept coming back to Waldo's 'refusal' to name the original source of the drug, or the other members of the ring. Waldo swore that he'd received no information except for the shipping details and knew nothing of any other people involved. It was a stand-off, but I could sense the jury tilting the wrong way. Innocence through ignorance is never a strong defense, and they could tell that it was contrary to Waldo's natural ego. The judge's summing-up, in which Waldo was painted as the leader of a desperate band of heartless villains, didn't help a bit.
The jury was out less than ten minutes. Guilty. Waldo, protesting his innocence, was sentenced to serve three years on Venus Station. I promised to wr
ite.
* * *
It's amazing how many people think, as I did, that the Venus terra-forming project is on Venus; actually that won't come for another three hundred years. All the work is done in orbit at Venus Station, seven hundred kilometers above the planet. The Station looks like two big wheels, four hundred meters across, on a common axle. I'd seen pictures of it, but that was all I knew until Waldo described it. The upper wheel, Station Up, spins—you get about one gee at the outer rim. It has all the hydroponics, air equipment and recycling equipment—and all the convicts. The lower wheel doesn't rotate. It's Station Down, and it acts as the docking facility and houses the algal seeders.
Waldo arrived at Station Down after a boring two-month flight from Earth, along with twenty other prisoners. I gather he was not impressed by his companions. They ranged from a mad bomber who had blown up the store that sold him a defective umbrella, to an illiterate janitor who had done in his wife when she refused to read stories to him. What annoyed Waldo was the way the rest of them looked down on him, as an unspeakable drug-master, destroyer of the young, perverter of the innocent. That, plus the fact that the bunks on the ship were designed for someone half his girth, made his life miserable. It shows how strange the world can be. A few months earlier, Waldo would have taken bets that he could never be glad to arrive at Venus Station to serve a prison sentence. But he saw Station Down swing into view with a great sense of relief.
After they docked he was taken to the Prison Admissions Office on Station Up. The work assignment supervisor there had a summary of Waldo's background, with the test results. He looked at them and shook his head.
"The only position I've got for you right now is as a Number Three Vatman, on the lower hydroponics level. One good thing about that, you'll have a gravity close to what you were used to on Earth. And it's a very important job; we all depend on the hydroponics."
Waldo frowned. It sounded as though it might be manual labor. He'd hoped for an administrative position—perhaps even a legal post.
"This vatman job. It doesn't sound as though it will make use of my skills. I'm sure I have the qualifications to fill a management slot for you here. Don't you have at least a clerical assignment available?"
"Not for your background." The supervisor looked sadly at Waldo's papers. "You have to understand, Mr. Burmeister, there's no shortage of lawyers in the prison. We have enough of you to fill all our clerical needs three times over. If you'd been a trained plumber now, or an electrician, that would be a different matter. You should find this job rewarding," he added, seeing Waldo's expression. "Recycling is a very important function. You'll have full control of all the stirring, filtering and additive operations on the Number Three vat line."
It was manual work all right. Waldo didn't like the sound of it at all.
"But what's in the vats?" he asked. "Just what is it you are recycling?"
The supervisor told him. Waldo liked the sound of it even less. He made one more try. "Look, there must be some other jobs open here. Surely all the prisoners don't have useful trades. There must be jobs here on the Station that don't correspond to anything back on Earth."
"Oh yes, there are. There's one vacancy right now for a scout ship operator. A very responsible position. They fly down into the atmosphere of Venus every day, and monitor the level that the algae reach before they become too hot to function. Unfortunately, that job has a weight limit." He looked at Waldo's bulk with misgiving. "You don't look less than ninety kilos, I'm afraid, so I didn't mention it to you."
Thank heaven for fat. Waldo mentally hugged his poundage to him. The last job he wanted was to be plunged into Venus' searing atmosphere as a sort of human dip stick. He should have kept his mouth shut.
"I'll keep your interest in the scout work in mind," the supervisor said encouragingly. "And don't worry about the vat work. I'm told that the smell is just a temporary problem. There's been something wrong with the chemical balance on the lowest level of tanks. Don't forget, in a year or so you'll be eligible for reassignment. I'll mark your interest in scouting down on your form here but I'm sure you'll soon settle in and make friends on the hydroponics work."
* * *
Curiously enough, the supervisor's optimistic prediction seemed to be right. The chief of the hydroponics area was a big bruiser named Katuki, who for some reason seemed delighted to see Waldo. He shook hands with enthusiasm and slapped him on the back.
"Hey, I'm really pleased to meet you, Mr. Burmeister. I've heard about you, but I didn't know you were going to be working down here. I thought it was impossible to rig the computers that assign people to different jobs. Sometime I'd like you to tell me how you worked it." Waldo smiled modestly.
"It's good to get a bit of class in the place," Katuki went on. "The other fellers are good guys, but I don't mind telling you some of them aren't the brightest. Stop by my area as soon as you're settled in, and I'll introduce you to the other vatmen."
Waldo was gratified. It was nice to be appreciated, even if the speaker's appearance was a little off-putting. At some time in the past Katuki's face seemed to have lost a major argument with something hard and irregular.
Waldo felt even more pleased later, when Katuki introduced him to the other four vatmen with a big build-up. No one had praised his brains so much for years. It's all relative, I suppose. A couple of others, according to Waldo, would have been hard pressed to decide which end of a stirring paddle to hold without guidance from Katuki.
Glasses and a bottle were produced from a locker and Katuki poured generous shots of a dark brown liquid. "Here's to our new buddy, Waldo Burmeister," he said, handing them around. "I know he's going to be a real help to the operation here."
Waldo hesitated, glass in hand, and looked at the door. "I'm sure you know best, but isn't this a bit risky? What about the guards?"
"Down here? You couldn't get a guard to the hydroponics levels unless you bribed him." Katuki thought for a moment. "I don't think I've seen one on this level for three months. Provided everything runs smoothly here, we're left to ourselves. Here's to you."
Waldo lifted his glass, expecting the worst, and gulped it down. He'd thought it would be near-beer, or rot-gut. It turned out to be high-proof, top quality bourbon. The others grinned at his obvious surprise.
"Not bad, eh, Waldo?" said Katuki. "I tell you, we do all right for ourselves down here. Know how we do it?"
Waldo accepted a second glass and thought for a moment. Obviously, they'd found a way to make or smuggle good booze. He didn't want to get involved in what might be a risky operation. On the other hand, he certainly didn't want to be cut off from the supply. This needed a careful answer.
"Mr. Katuki, when a lawyer is asked if he was given a piece of information, he's legally obliged to answer, yes or no. But he can't be asked what he or somebody else was thinking. So to answer your question, I'd rather not be told where the drink comes from."
There was a baffled silence for a few seconds as the gears ground inside Katuki's bullet head. Then his face lit up. "Hey, I like that." He turned to the others. "See how to do it. No talk, no chance to get caught out." Then to Waldo. "You'll get the picture for yourself soon enough, when we look around the works tomorrow."
The next day wasn't so good. Despite Katuki's pride in the set-up, the three hydroponics levels were a bit stark. They began with the algae breeding tanks on the third level, where the big vats were cultured for the seeders.
"We pipe 'em to Station Down as soon as they're ready," explained Katuki. "Then the seeders spray the algae out into the upper atmosphere. They convert carbon dioxide to oxygen as they fall, and die when it gets too hot for them. Each time we go over the same spot on the ground, the algae get a bit lower before they're crisped. It's already a couple of degrees cooler down on the surface than it was when the project started."
Waldo suppressed a yawn. Technology bored him. They went down a staircase to the second level and then along a corridor that led to the second le
vel hydroponics tanks. Katuki had got a little more jumpy, excited about something. He kept glancing at Waldo as though in anticipation.
"Don't ever touch that red lever on the wall unless I tell you," he warned as they came halfway along the corridor. "It opens up a section of the floor, so we can dump chemicals into the channel on the first level."
"What's in the channel?"
"Partly treated sewage, on its way through the lowest level hydroponics tanks. You wouldn't drown if you fell down there—it's only waist-deep. I don't think you'd enjoy it, though."
They walked on, Waldo treading very gingerly as they went over the trapdoor section of the corridor. Just before the staircase to the lowest level Katuki stopped and looked into a small room on the left. It was filled with long spirals of silver coils, winding halfway to the ceiling. It looked curiously familiar. As they came down the staircase and out to the lowest level hydroponics, Waldo had a sudden insight.
A still. That's what those metal coils had to be, and that's where the liquor was coming from. As they walked past the fronded, blue-green plants of the long hydroponics tank he noticed that Katuki was looking at him with a sly, expectant air. Waldo winked and Katuki grinned back at him.
"We don't need to talk about it, right, Waldo?" he said. "A wink's as good as a nod to a blind horse."
They moved out along the first level catwalk, with the big hydroponics tank on their left. A broad stream of grey-green sewage, with beaded bubbles winking at the brim, moved sluggishly past on the right. Katuki noticed Waldo's expression and grinned again.
"That's where you finish up if you fall through the second level trapdoor. Don't make any enemies among the other vatmen, Waldo."
Waldo looked again at the steaming mess and shuddered. His appetite for dinner dropped a notch.
After a month he had the working routine mastered, but his taste for the job didn't increase. As far as Waldo was concerned, a vatman's lot was not a happy one. Apart from Katuki, the vatmen were near-morons and a grunt passed for sparkling conversation. What with filtering, stirring, removing sludge and adding chemicals, Waldo had lost ten kilos and was beginning to regard a human being as no more than an instrument for recycling sewage. That was a pity, because the vatmen under Katuki's direction dined—and wined—amazingly well. The third level of tanks were dedicated to producing algae for the seeders, and the lowest level next to the bottom sewage channel was used for oxygen production. But part of the tank on the second level had been set up as a kitchen garden and produced excellent vegetables.
Vectors Page 11