Schwarzschild Radius Read online

  Schwarzschild Radius

  Connie Willis

  Nominated for the Nebula Award for Best Novelette in 1987.

  Connie Willis

  Schwarzschild Radius

  When a star collapses, it sort of falls in on itself.” Travers curved his hand into a semicircle and then brought the fingers in. “And sometimes it reaches a kind of point of no return where the gravity pulling in on it is stronger than the nuclear and electric forces, and when it reaches that point, nothing can stop it from collapsing and it becomes a black hole.” He closed his hand into a fist. “And that critical diameter, that point where there’s no turning back, is called the Schwarzschild radius.” Travers paused, waiting for me to say something.

  He had come to see me every day for a week, sitting stiffly on one of my chairs in an unaccustomed shirt and tie, and talked to me about black holes and relativity, even though I taught biology at the university before my retirement, not physics. Someone had told him I knew Schwarzschild, of course.

  “The Schwarzschild radius?” I said in my quavery, old man’s voice, as if I could not remember ever hearing the phrase before, and Travers looked disgusted. He wanted me to say, “The Schwarzschild radius! Ah, yes, I served with Karl Schwarzschild on the Russian front in World War I!” and tell him all about how he had formulated his theory of black “holes while serving with the artillery, but I had not decided yet what to tell him. “The event horizon,” I said.

  “Yeah. It was named after Schwarzschild because he was the one who worked out the theory,” Travers said. He reminded me of Müller with his talk of theories. He was the same age as Müller, with the same shock of stiff yellow hair and the same insatiable curiosity, and perhaps that was why I let him come every day to talk to me, though it was dangerous to let him get so close.

  “I have drawn up a theory of the stars,” Müller says while we warm our hands over the Primus stove so that they will get enough feeling in them to be able to hold the liquid barretter without dropping it. “They are not balls of fire, as the scientists say. They are frozen.”

  “How can we see them if they are frozen?” I say. Müller is insulted if I do not argue with him. The arguing is part of the theory.

  “Look at the wireless!” he says, pointing to it sitting disemboweled on the table. We have the back off the wireless again, and in the barretter’s glass tube is a red reflection of the stove’s flame. “The light is a reflection off the ice of the star.”

  “A reflection of what?”

  “Of the shells, of course.”

  I do not say that there were stars before there was this war, because Müller will not have an answer to this, and I have no desire to destroy his theory, and besides, I do not really believe there was a time when this war did not exist. The star shells have always exploded over the snow-covered craters of No Man’s Land, shattering in a spray of white and red, and perhaps Müller’s theory is true.

  “At that point,” Travers said, “at the event horizon, no more information can be transmitted out of the black hole because gravity has become so strong, and so the collapse appears frozen at the Schwarzschild radius.”

  “Frozen,” I said, thinking of Müller.

  “Yeah. As a matter of fact, the Russians call black holes ‘frozen stars.’ You were at the Russian front, weren’t you?”

  “What?”

  “In World War I.”

  “But the star doesn’t really freeze,” I said. “It goes on collapsing.”

  “Yeah, sure,” Travers said. “It keeps collapsing in on itself until even the atoms are stripped of their electrons and there’s nothing left except what they call a naked singularity, but we can’t see past the Schwarzschild radius, and nobody inside a black hole can tell us what it’s like in there because they can’t get messages out, so nobody can ever know what it’s like inside a black hole.”

  “I know,” I said, but he didn’t hear me.

  He leaned forward. “What was it like at the front?”

  It is so cold we can only work on the wireless a few minutes at a time before our hands stiffen and grow clumsy, and we are afraid of dropping the liquid barretter. Müller holds his gloves over the Primus stove and then puts them on. I jam my hands into my ice-stiff pockets.

  We are fixing the wireless set. Eisner, who had been delivering messages between the sectors, got sent up to the front when he could not fix his motorcycle. If we cannot fix the wireless, we will cease to be telegraphists and become soldiers, and we will be sent to the front lines.

  We are already nearly there. If it were not snowing, we could see the barbed wire and pitted snow of No Man’s Land, and the big Russian coal boxes sometimes land in the communication trenches. A shell hit our wireless hut two weeks ago. We are ahead of our own artillery lines, and some of the shells from our guns fall on us, too,because the muzzles are worn out. But it is not the front, and we guard the liquid barretter with our lives.

  “Eisner’s unit was sent up on wiring fatigue last night,” Müller says, “and they have not come back. I have a theory about what happened to them.”

  “Has the mail come?” I say, rubbing my sore eyes and then putting my cold hands immediately back in my pockets. I must get some new gloves, but the quartermaster has none to issue. T have written my mother three times to knit me a pair, but she has not sent them yet.

  “I have a theory about Eisner’s unit,” he says doggedly. “The Russians have a magnet that has pulled them into the front.”

  “Magnets pull iron, not people,” I say.

  I have a theory about Müller’s theories. Littering the communications trenches are things that the soldiers going up to the front have discarded: water bottles and haversacks and bayonets. Hans and I sometimes tried to puzzle out why they would discard such important things.

  “Perhaps they were too heavy,” I would say, though that did not explain the bayonets or the boots.

  “Perhaps they know they are going to die,” Hans would say, picking up a helmet.

  I would try to cheer him up. “My gloves fell out of my pocket yesterday when I went to the quartermaster’s. I never found them. They are in this trench somewhere.”

  “Yes,” he would say, turning the helmet round and round in his hands, “perhaps as they near the front, these things simply drop away from them.”

  My theory is that what happens to the water bottles and helmets and bayonets is what has happened to Müller. He was a student in university before the war, but his knowledge of science and his intelligence have fallen away from him, and now we are so close to the front, all he has left are his theories. And his curiosity, which is a dangerous thing to have kept.

  “Exactly. Magnets pull iron, and they were carrying barbed wire!” he says triumphantly. “And so they were pulled in to the magnet.”

  I put my hands practically into the Primus flame and rub them together, trying to get rid of the numbness. “We had better get the barretter in the wireless again or this magnet of yours will suck it to the front, too.”

  I go back to the wireless. Müller stays by the stove, thinking about his magnet. The door bangs open. It is not a real door, only an iron humpie tied to the beam that reinforces the dugout and held with a wedge, and when someone pushes against it, it flies inward, bringing the snow with it.

  Snow swirls in, and light, and the sound from the front, a low rumble like a dog growling. I clutch the liquid barretter to my chest, and Müller flings himself over the wireless as if it were a wounded comrade. Someone bundled in a wool coat and mittens, with a wool cap pulled over his ears, stands silhouetted against the reddish light in the doorway, blinking at us.

  “Is Private Rottschieben here? I have come to see him about his eyes,” he says,
and I see it is Dr. Funkenheld.

  “Come in and shut the door,” I say, still carefully protecting the liquid barretter, but Müller has already jammed the metal back against the beam.

  “Do you have news?” Müller says to the doctor, eager for new facts to spin his theories from. “Has the wiring fatigue come back? Is there going to be a bombardment tonight?”

  Dr. Funkenheld takes off his mittens. “I have come to examine your eyes,” he says to me. His voice frightens me. All through the war he has kept his quiet bedside voice, speaking to the wounded in the dressing station and at the stretcher bearer’s posts as if they were in his surgery in Stuttgart, but now he sounds agitated, and I am afraid it means a bombardment is coming and he will need me at the front.

  When I went to the dressing station for medicine for my eyes, I foolishly told him I had studied medicine with Dr. Zuschauer in Jena. Now I am afraid he will ask me to assist him, which will mean going up to the front. “Do your eyes still hurt?” he says.

  I hand the barretter to Müller and go over to stand by the lantern that hangs from a nail in the beam.

  “I think he should be invalided home, Herr Doktor,” Müller says. He knows it is impossible, of course. He was at the wireless the day the message came through that no one was to be invalided out for frostbite or “other non-contagious diseases.”

  “Can you find me a better light?” the doctor says to him.

  Müller’s curiosity is so strong that he cannot bear to leave any place where something interesting is happening. If he went up to the front, I do not think he would be able to pull himself away, and now I expect him to make some excuse to stay, but I have forgotten that he is even more curious about the wiring fatigue. “I will go see what has happened to Eisner’s unit,” he says, and opens the door. Snow flies in, as if it had been beating against the door to get in, and the doctor and I have to push against the door to get it shut again.

  “My eyes have been hurting,” I say, while we are still pushing the metal into place, so that he cannot ask me to assist him. “They feel like sand has gotten into them.”

  “I have a patient with a disease I do not recognize,” he says. I am relieved, though disease can kill us as easily as a trench mortar. Soldiers die of pneumonia and dysentery and blood poisoning every day in the dressing station, but we do not fear it the way we fear the front.

  “The patient has fever, excoriated lesions, and suppurating bullae,” Dr. Funkenheld says.

  “Could it be boils?” I say, though of course he would recognize something so simple as boils, but he is not listening to me, and I realize that it is not a diagnosis from me that he has come for.

  “The man is a scientist, a Jew named Schwarzschild, attached to the artillery,” he says, and because the artillery are even farther back from the front lines than we are, I volunteer to go and look at the patient, but he does not want that either.

  “I must talk to the medical headquarters in Bialystok,” he says.

  “Our wireless is broken,” I say, because I do not want to have to tell him why it is impossible for me to send a message for him. We are allowed to send only military messages, and they must be sent in code, tapped out on the telegraph key. It would take hours to send his message, even if it were possible. I hold up the dangling wire. “At any rate, you must clear it with the commandant,” but he is already writing out the name and address on a piece of paper, as if this were a telegraph office.

  “You can send the message when you get the wireless fixed. I have written out the symptoms.”

  I put the back on the wireless. Müller comes in, kicking the door open, and snow flies everywhere, picking up Dr. Funkenheld’s message and sending it circling around the dugout. I catch it before it spirals into the flame of the Primus stove.

  “The wiring fatigue was pinned down all night,” Müller says, setting down a hand lamp. He must have gotten it from the dressing station. “Five of them froze to death, the other eight have frostbite. The commandant thinks there may be a bombardment tonight.” He does not mention Eisner, and he does not say what has happened to the rest of the thirty men in Eisner’s unit, though I know. The front has gotten them. I wait, holding the message in my stiff fingers, hoping Dr. Funkenheld will say, “I must go attend to their frostbite.”

  “Let me examine your eyes,” the doctor says, and shows Müller how to hold the hand lamp. Both of them peer into my eyes. “I have an ointment for you to usetwice daily,” he says, getting a flat jar out of his bag. “It will burn a little.”

  “I will rub it on my hands then. It will warm them,” I say, thinking of Eisner frozen at the front, still holding the roll of barbed wire, perhaps.

  He pulls my bottom eyelid down and rubs the ointment on with his little finger. It does not sting, but when I have blinked it into my eye, everything has a reddish tinge. “Will you have the wireless fixed by tomorrow?” he says.

  “I don’t know. Perhaps.”

  Müller has not put down the hand lamp. I can see by its light that he has forgotten all about the wiring fatigue and the Russian magnet and is wondering what the doctor wants with the wireless.

  The doctor puts on his mittens and picks up his bag. I realize too late I should have told him I would send the message in exchange for them. “I will come check your eyes tomorrow,” he says, and opens the door to the snow. The sound of the front is very close.

  As soon as he is gone, I tell Müller about Schwarzschild and the message the doctor wants to send. He will not let me rest until I have told him, and we do not have time for his curiosity. We must fix the wireless.

  “If you were on the wireless, you must have sent messages for Schwarzschild,” Travers said eagerly. “Did you ever send a message to Einstein? They’ve got the letter Einstein sent to him after he wrote him his theory, but if Schwarzschild sent him some kind of message, too, that would be great. It would make my paper.”

  “You said that no message can escape a black hole?” I said. “But they could escape a collapsing star. Is that not so?”

  “Okay,” Travers said impatiently, and made his fingers into a semicircle again. “Suppose you have a fixed observer over here.” He pulled his curved hand back and held the forefinger of his other hand up to represent the fixed observer. “And you have somebody in the star. Say when the star starts to collapse, the person in it shines a light at the fixed observer. If the star hasn’t reached the Schwarzschild radius, the fixed observer will be able to see the light, but it will take longer to reach him because the gravity of the black hole is pulling on the light, so it will seem as if time on the star has slowed down, and the wavelengths will have been lengthened, so the light will be redder. Of course that’s just a thought problem. There couldn’t really be anybody in a collapsing star to send the messages.”

  “We sent messages,” I said. “I wrote my mother asking her to knit me a pair of gloves.”

  There is still something wrong with the wireless. We have received only one message in two weeks. It said, “Russian opposition collapsing,” and there was so much static we could not make out the rest of it. We have taken the wireless apart twice. The first time we found a loose wire, but the second time we could not find anything. If Hans were here, he would be able to find the trouble immediately.

  “I have a theory about the wireless,” Müller says. He has had ten theories in as many days: The magnet of the Russians is pulling our signals in to it; the northern lights, which have been shifting uneasily on the horizon, make a curtain the wireless signals cannot get through; the Russian opposition is not collapsing at all. They are drawing us deeper and deeper into a trap.

  I say, “I am going to try again. Perhaps the trouble has cleared up,” and put the headphones on so I do not have to listen to his new theory. I can hear nothing but a rumbling roar that sounds like the front.

  I take out the folded piece of paper Dr. Funkenheld gave me and lay it on the wireless. He comes nearly every night to see if I have gotten an answer
to his message, and I take off the headphones and let him listen to the static. I tell him that we cannot get through, but even though that is true, it is not the real reason I have not sent the message. I am afraid of the commandant finding out. I am afraid of being sent to the front.

  I have compromised by writing a letter to the professor that I studied medicine with in Jena, but I have not gotten an answer from him yet, and so I must go on pretending to the doctor.

  “You don’t have to do that,” Müller says. He sits on the wireless, swinging his leg. He picks up the paper with the symptoms on it and holds it to the flame of the Primus stove. I grab for it, but it is already burning redly. “I have sent the message for you.”

  “I don’t believe you. Nothing has been getting out.”

  “Didn’t you notice the northern lights did not appear last night?”

  I have not noticed. The ointment the doctor gave to me makes everything look red at night, and I do not believe in Müller’s theories. “Nothing is getting out now,” I say, and hold the headphones out to him so he can hear the static. He listens, still swinging his leg. “You will get us both in trouble. Why did you do it?”

  “I was curious about it.” If we are sent up to the front, his curiosity will kill us. He will take apart a land mine to see how it works. “We cannot get in trouble for sending military messages. I said the commandant was afraid it was a poisonous gas the Russians were using.” He swings his leg and grins because now 1 am the curious one.

  “Well, did you get an answer?”

  “Yes,” he says maddeningly, and puts the headphones on. “It is not a poisonous gas.”

  I shrug as if I do not care whether I get an answer or not. I put on my cap and the muffler my mother knitted for me and open the door. “I am going out to see if themail has come. Perhaps there will be a letter there from my, professor.”

  “Nature of disease unknown,” Müller shouts against the sudden force of he snow. “Possibly impetigo or glandular disorder.”