“So the first one’s suspended?”
“No. She woke as soon as she arrived.”
That seemed even stranger than their excess baggage. If you were travelling with someone, why not delay activation until your companion caught up? Or better yet, package yourselves as interleaved bits?
“But she’s still in the arrival lounge?”
“Yes.”
Gisela hesitated. “Shouldn’t I wait until the other one’s all here? So I can greet them together?”
“No.” The mayor seemed confident on this point. Gisela wished interpolis protocol allowed non-sentient software to play host; she felt woefully ill-prepared for the role, herself. But if she started consulting people, seeking advice, and looking into Athena’s culture in depth, the visitors would probably have toured Cartan and gone home before she was ready for them.
She steeled herself, and jumped.
***
The last person who’d whimsically redesigned the arrival lounge had made it a wooden pier surrounded by grey, windswept ocean. The first of the two visitors was still standing patiently at the end of the pier, which was just as well; it was unbounded in the other direction, and walking a few kilodelta to no avail might have been a bit dispiriting. Her fellow traveller, still in transit, was represented by a motionless placeholder. Both icons were highly anatomical-realist, clothed but clearly male and female, the unfrozen female much younger-looking. Gisela’s own icon was more stylised, and her surface, whether “skin” or “clothing” — either could gain a tactile sense if she wished — was textured with diffuse reflection rules not quite matching the optical properties of any real substance.
“Welcome to Cartan. I’m Gisela.” She stretched out her hand, and the visitor stepped forward and shook it — though it was possible that she perceived and executed an entirely different act, cross-translated through gestural interlingua.
“I’m Cordelia. This is my father, Prospero. We’ve come all the way from Earth.” She seemed slightly dazed, a response Gisela found entirely reasonable. Back in Athena, whatever elaborate metaphoric action they’d used to instruct the communications software to halt them, append suitable explanatory headers and checksums, then turn the whole package bit-by-bit into a stream of modulated gamma rays, it could never have fully prepared them for the fact that in a subjective instant they’d be stepping ninety-seven years into the future, and ninety-seven light years from home.
“You’re here to observe the Planck Dive?” Gisela chose to betray no hint of puzzlement; it would have been pointlessly cruel to drive home the fact that they could have seen everything from Athena. Even if you fetishised realtime data over lightspeed transmissions, it could hardly be worth slipping one-hundred-and-ninety-four years out of synch with your fellow citizens.
Cordelia nodded shyly, and glanced at the statue beside her. “My father, really … ”
Meaning what? It was all his idea? Gisela smiled encouragingly, hoping for clarification, but none was forthcoming. She’d been wondering why a Prospero had named his daughter Cordelia, but now it struck her as only prudent — if you had to succumb to a Shakespearean names fad at all — not to put anyone from the same play together in one family.
“Would you like to look around? While you’re waiting for him?”
Cordelia stared at her feet, as if the question was profoundly embarrassing.
“It’s up to you.” Gisela laughed. “I have no idea what constitutes the polite treatment of half-delivered relatives.” It was unlikely that Cordelia did, either; citizens of Athena clearly didn’t make a habit of crossing interstellar distances, and the connections on Earth all had so much bandwidth that the issue would never arise. “But if it was me in transit, I wouldn’t mind at all.”
Cordelia hesitated. “Could I see the black hole, please?”
“Of course.” Chandrasekhar possessed no blazing accretion disk — it was six billion years old, and had long ago swept the region clean of gas and dust — but it certainly left the imprint of its presence on the ordinary starlight around it. “I’ll give you the short tour, and we’ll be back long before your father’s awake.” Gisela examined the bearded icon; with his gaze fixed on the horizon and his arms at his sides, he appeared to be on the verge of bursting into song. “Assuming he’s not running on partial data already. I could have sworn I saw those eyes move.”
Cordelia smiled slightly, then looked up and said solemnly, “That’s not how we were packaged.”
Gisela sent her an address tag. “Then he’ll be none the wiser. Follow me.”
***
They stood on a circular platform in empty space. Gisela had inflected the scape’s address to give the platform “artificial gravity” — a uniform one gee, regardless of their motion — and a transparent dome full of air at standard temperature and pressure. Presumably all Athena citizens were set up to ignore any scape parameters that might cause them discomfort, but it still seemed like a good idea to err on the side of caution. The platform itself was a compromise, five delta wide — offering some protection from vertigo, but small enough to let its occupants see some forty degrees below “horizontal.”
Gisela pointed. “There it is: Chandrasekhar. Twelve solar masses. Seventeen thousand kilometres away. It might take you a moment to spot it; it looks about the same as the new moon from Earth.” She’d chosen their coordinates and velocity carefully; as she spoke, a bright star split in two, then flared for a moment into a small, perfect ring as it passed directly behind the hole. “Apart from gravitational lensing, of course.”
Cordelia smiled, obviously delighted. “Is this a real view?”
“Partly. It’s based on all the images we’ve received so far from a whole swarm of probes — but there are still viewpoints that have never been covered, and need to be interpolated. That includes the fact that we’re almost certainly moving with a different velocity than any probe that passed through the same location — so we’re seeing things differently, with different Doppler shifts and aberration.”
Cordelia absorbed this with no sign of disappointment. “Can we go closer?”
“As close as you like.”
Gisela sent control tags to the platform, and they spiralled in. For a while it looked as if there’d be nothing more to see; the featureless black disk ahead of them grew steadily larger, but it clearly wasn’t going to blossom with any kind of detail. Gradually though, a congested halo of lensed images began to form around it, and you didn’t need the flash of an Einstein ring to see that light was behaving strangely.
“How far away are we now?”
“About thirty-four M.” Cordelia looked uncertain. Gisela added, “Six hundred kilometres — but if you convert mass into distance in the natural way, that’s thirty-four times Chandrasekhar’s mass. It’s a useful convention; if a hole has no charge or angular momentum, its mass sets the scale for all the geometry: the event horizon is always at two M, light forms circular orbits at three M, and so on.” She conjured up a spacetime map of the region outside the hole, and instructed the scape to record the platform’s world line on it. “Actual distances travelled depend on the path you take, but if you think of the hole as being surrounded by spherical shells on which the tidal force is constant — something tangible you can measure on the spot — you can give them each a radius of curvature without caring about the details of how you might travel all the way to their centre.” With one spatial dimension omitted to make room for time, the shells became circles, and their histories on the map were shown as concentric translucent cylinders.
As the disk itself grew, the distortion around it spread faster. By ten M, Chandrasekhar was less than sixty degrees wide, but even constellations in the opposite half of the sky were visibly crowded together, as incoming light rays were bent into more radial paths. The gravitational blue shift, uniform across the sky, was strong enough now to give the stars a savage glint — not so much icy, as blue-hot. On the map, the light cones dotted along their world li
ne — structures like stylised conical hour-glasses, made up of all the light rays passing through a given point at a given moment — were beginning to tilt towards the hole. Light cones marked the boundaries of physically possible motion; to cross your own light cone would be to outrace light.
Gisela created a pair of binoculars and offered them to Cordelia. “Try looking at the halo.”
Cordelia obliged her. “Ah! Where did all those stars come from?”
“Lensing lets you see the stars behind the hole, but it doesn’t stop there. Light that grazes the three-M shell orbits part-way around the hole before flying off in a new direction — and there’s no limit to how far it can swing around, if it grazes the shell close enough.” On the map, Gisela sketched half a dozen light rays approaching the hole from various angles; after wrapping themselves in barber’s-pole helices at slightly different distances from the three-M cylinder, they all headed off in almost the same direction. “If you look into the light that escapes from those orbits, you see an image of the whole sky, compressed into a narrow ring. And at the inner edge of that ring, there’s a smaller ring, and so on — each made up of light that’s orbited the hole one more time.”
Cordelia pondered this for a moment. “But it can’t go on forever, can it? Won’t diffraction effects blur the pattern, eventually?”
Gisela nodded, hiding her surprise. “Yeah. But I can’t show you that here. This scape doesn’t run to that level of detail!”
They paused at the three-M shell itself. The sky here was perfectly bisected: one hemisphere in absolute darkness, the other packed with vivid blue stars. Along the border, the halo arched over the dome like an impossibly geometricised Milky Way. Shortly after Cartan’s arrival, Gisela had created an hommage to Escher based on this view, tiling the half-sky with interlocking constellations that repeated at the edge in ever-smaller copies. With the binoculars on 1000 X, they could see a kind of silhouette of the platform itself “in the distance”: a band of darkness blocking a tiny part of the halo in every direction.
Then they continued towards the event horizon — oblivious to both tidal forces and the thrust they would have needed to maintain such a leisurely pace in reality.
The stars were now all brightest at ultraviolet frequencies, but Gisela had arranged for the dome to filter out everything but light from the flesher visible spectrum, in case Cordelia’s simulated skin took descriptions of radiation too literally. As the entire erstwhile celestial sphere shrank to a small disk, Chandrasekhar seemed to wrap itself around them — and this optical illusion had teeth. If they’d fired off a beam of light away from the hole, but failed to aim it at that tiny blue window, it would have bent right around like the path of a tossed rock and dived back into the hole. No material object could do better; the choice of escape routes was growing narrower. Gisela felt a frisson of claustrophobia; soon she’d be doing this for real.
They paused again to hover — implausibly — just above the horizon, with the only illumination a pin-prick of heavily blue-shifted radio waves behind them. On the map, their future light cone led almost entirely into the hole, with just the tiniest sliver protruding from the two-M cylinder. Gisela said, “Shall we go through?”
Cordelia’s face was etched in violet. “How?”
“Pure simulation. As authentic as possible … but not so authentic that we’ll be trapped, I promise.”
Cordelia spread her arms, closed her eyes, and mimed falling backwards into the hole. Gisela instructed the platform to cross the horizon.
The speck of sky blinked out, then began to expand again, rapidly. Gisela was slowing down time a millionfold; in reality they would have reached the singularity in a fraction of a millisecond.
Cordelia said, “Can we stop here?”
“You mean freeze time?”
“No, just hover.”
“We’re doing that already. We’re not moving.” Gisela suspended the scape’s evolution. “I’ve halted time; I think that’s what you wanted.”
Cordelia seemed about to dispute this, but then she gestured at the now-frozen circle of stars. “Outside, the blue shift was the same right across the sky … but now the stars at the edge are much bluer. I don’t understand.”
Gisela said, “In a way it’s nothing new; if we’d let ourselves free-fall towards the hole, we would have been moving fast enough to see a whole range of Doppler shifts superimposed on the gravitational blue shift, long before we crossed the horizon. You know the starbow effect?”
“Yes.” Cordelia examined the sky again, and Gisela could almost see her testing the explanation, imagining how a blue-shifted starbow should look. “But that only makes sense if we’re moving — and you said we weren’t.”
“We’re not, by one perfectly good definition. But it’s not the definition that applied outside.” Gisela highlighted a vertical section of their world line, where they’d hovered on the three-M shell. “Outside the event horizon — given a powerful enough engine — you can always stay fixed on a shell of constant tidal force. So it makes sense to choose that as a definition of being ‘motionless’ — making time on this map strictly vertical. But inside the hole, that becomes completely incompatible with experience; your light cone tilts so far that your world line must cut through the shells. And the simplest new definition of being ‘motionless’ is to burrow straight through the shells — the complete opposite of trying to cling to them — and to make ‘map time’ strictly horizontal, pointing towards the centre of the hole.” She highlighted a section of their now-horizontal world line.
Cordelia’s expression of puzzlement began to give way to astonishment. “So when the light cones tip over far enough … the definitions of ‘space’ and ‘time’ have to tip with them?”
“Yes! The centre of the hole lies in our future, now. We won’t hit the singularity face-first, we’ll hit it future-first — just like hitting the Big Crunch. And the direction on this platform that used to point towards the singularity is now facing ‘down’ on the map — into what seems from the outside to be the hole’s past, but is really a vast stretch of space. There are billions of light years laid out in front of us — the entire history of the hole’s interior, converted into space — and it’s expanding as we approach the singularity. The only catch is, elbow room and head room are in short supply. Not to mention time.”
Cordelia stared at the map, entranced. “So the inside of the hole isn’t a sphere at all? It’s a spherical shell in two directions, with the shell’s history converted into space as the third … making the whole thing the surface of a hypercylinder? A hypercylinder that’s increasing in length, while its radius shrinks.” Suddenly her face lit up. “And the blue shift is like the blue shift when the universe starts contracting?” She turned to the frozen sky. “Except this space is only shrinking in two directions — so the more the angle of the starlight favours those directions, the more it’s blue-shifted?”
“That’s right.” Gisela was no longer surprised by Cordelia’s rapid uptake; the mystery was how she could have failed to learn everything there was to know about black holes, long ago. With unfettered access to a half-decent library and rudimentary tutoring software, she would have filled in the gaps in no time. But if her father had dragged her all the way to Cartan just to witness the Planck Dive, how could he have stood by and allowed Athena’s culture to impede her education? It made no sense.
Cordelia raised the binoculars and looked sideways, around the hole. “Why can’t I see us?”
“Good question.” Gisela drew a light ray on the map, aimed sideways, leaving the platform just after they’d crossed the horizon. “At the three-M shell, a ray like this would have followed a helix in spacetime, coming back to our world line after one revolution. But here, the helix has been flipped over and squeezed into a spiral — and at best, it only has time to travel half-way around the hole before it hits the singularity. None of the light we’ve emitted since crossing the horizon can make it back to us.
&nb
sp; “That’s assuming a perfectly symmetrical Schwarzschild black hole, which is what we’re simulating. And an ancient hole like Chandrasekhar probably has settled down to a fair approximation of the Schwarzschild geometry. But close to the singularity, even infalling starlight would be blue-shifted enough to disrupt it, and anything more massive — like us, if we really were here — would cause chaotic changes even sooner.” She instructed the scape to switch to Belinsky-Khalatnikov-Lifshitz geometry, then restarted time. The stars began to shimmer with distortion, as if seen through a turbulent atmosphere, then the sky itself seemed to boil, red shifts and blue shifts sweeping across it in churning waves. “If we were embodied, and strong enough to survive the tidal forces, we’d feel them oscillating wildly as we passed through regions collapsing and expanding in different directions.” She modified the spacetime map accordingly, and enlarged it for a better view. Close to the singularity, the once-regular cylinders of constant tidal force now disintegrated into a random froth of ever finer, ever more distorted bubbles.
Cordelia examined the map with an expression of consternation. “How are you going to do any kind of computation in an environment like that?”
“We’re not. This is chaos — but chaotic systems are highly susceptible to manipulation. You know Tiplerian theology? The doctrine that we should try to reshape the universe to allow infinite computation to take place before the Big Crunch?”
“Yes.”
Gisela spread her arms to take in all of Chandrasekhar. “Reshaping a black hole is easier. With a closed universe, all you can do is rearrange what’s already there; with a black hole, you can pour new matter and radiation in from all directions. By doing that, we’re hoping to steer the geometry into a more orderly collapse — not the Schwarzschild version, but one that lets light circumnavigate the space inside the hole many times. Cartan Null will be made of counter-rotating beams of light, modulated with pulses like beads on a string. As they pass through each other, the pulses will interact; they’ll be blue-shifted to energies high enough for pair-production, and eventually even high enough for gravitational effects. Those beams will be our memory, and their interactions will drive all our computation — with luck, down almost to the Planck scale: ten-to-the-minus-thirty-five metres.”
Anthology of Speculative Fiction, Volume Two Page 287
