Timelike Infinity

'But, Jaar—' She shook her head. 'Your Project has nearly brought disaster down on us all already. Hasn’t it? You mustn’t lose sight of this simple fact, my friend — we were lucky to defeat the Qax invasion from the future. If they hadn’t been so slow to react, so complacent, so sure we had no threat to offer them — then they could have destroyed the race. Is your Project worth such a risk again?'

Jaar replied with intensity, 'Berg, your words in the singularity chamber, at the height of the struggle with the Spline — that I must survive, in order to fight another day, to continue with the Project — changed me, convinced me. Yes, the Project is worth all of that. It’s worth any risk — believe me, any price.'

'Look, I said all that when the roof was caving in. Literally. It was a ploy, Jaar. I was trying to manipulate you, to get you to fight, to make you do what I wanted you to do.'

'I know that.' He smiled. 'Of course I know that. But the motives behind your words don’t reduce their truth. Don’t you see that?'

She studied his long, certain face, and wrapped her arms closely around her, troubled.

* * *

Harry Poole, downloaded into the nervous system of the Spline, was in agony.

Jesus Christ -

The Spline’s body and sensorium encased him like the inside of his own (corporeal) head. He felt its vast, intimidating bulk all around him; the toughened outer flesh-hull felt as if it were third- degree burnt; the weapons and sensor spots were like open wounds.

The Spline must be in constant, continual pain, he realized; yes, they had been adapted for survival in space and hyperspace, but clumsily, he saw now. He felt like an amputee, nerve ends crudely welded to steamhammers and jacks.

Was this a price worth paying, even for special longevity?… and the Qax must have endured this horror too. Then again, he thought, perhaps pain had a different meaning for one as alien as a Qax.

In addition to the routine life agonies of the Spline there was more torment: from the half-healed wounds in the hull inflicted by its close encounter with the exotic material of the Interface portal; from the wreckage of the Crab that was still lodged within the Spline’s fleshy bulk like a clumsy arrow.

The shock of Poole’s crude attack had been enough to kill the Spline. The pain Harry suffered now was like the agony of a new birth, into a universe of darkness and terror.

…And yet, as he became accustomed to the size and scale of the Spline, to the constant, wailing screech of pain, Harry became aware of — compensating factors.

Some of his sensors — even some of the Spline’s ancient, original eyes, like the one ravaged by Jasoft Parz — still worked. He saw the stars through the eyes of a sentient starship; they were remote yet accessible, like youthful ideals. He could still turn; the Spline could roll. Vast, hidden flywheels of bone moved somewhere inside him, and space slid past his hull; he felt the centrifugal wrench of rotation as if the stars themselves were rolling around him, tugging.

And burning like a fire in his gut, he felt the power of the hyperdrive. Cautiously he flexed those strange, indirect muscles; and he thrilled at the power he could direct — the power to unravel the dimensions of spacetime itself.

Yes, there was grandeur to be a Spline.

He opened pixel eyes inside the lifedome of the wrecked Crab. His son was staring up at him. 'I can fly,' Harry said.

* * *

Jasoft Parz had shed his skinsuit, snakelike; now he floated in the air, one of Michael’s roomier dressing gowns billowing around him. 'From what your companion Berg reports, these Friends of Wigner sound determined to revive their Project.'

Michael Poole lay back in his couch in the Crab’s lifedome and steepled his fingers behind his head. 'But the Friends are going to need access to singularity manufacturing technology on an industrial scale, if they are to rebuild their earth-craft. And that surely means keeping the Interface access to the future open. We simply don’t have the infrastructure for such an endeavor, in this time period.'

Harry, his huge Virtual head floating in the air above Poole’s couch, nodded wisely. 'But then we’re leaving the door unlocked against whatever else the Qax choose to throw down their wormhole pipe at us. Not to mention any companions of Miss Splendid Isolation over there.' He nodded toward Shira; the girl from the earth-craft sat at a data console scrolling idly through some of Michael’s research results, studiously ignoring the conversation.

Parz said, 'The Qax were utterly complacent in their invasion of this time frame. And so — perhaps — no message, no report of the disaster, was sent back through the Interface to my era. But the Qax Occupation authorities will surely send through more probes, to investigate the outcome. We have bought time with our victory; but no more, as long as the Interface remains open.'

Shira looked up; Michael absently noted how the light of Jupiter highlighted the graceful curves of her shaven cranium. 'Are you so sure you can close the portal?' she asked quietly. 'You designed it, Michael Poole; you must know that spacetime wormholes are not hinged hatches one can open and close at will.'

'We’ll find a way, if we have to,' Michael said seriously.

'And if the Qax, or the Friends of the future, choose not to allow it?'

'Believe me. We’ll find a way.'

Parz nodded, his green eyes narrow. 'Yes. But perhaps we should begin considering now how to do such a thing. We may need the option rapidly, should we decide to use it — or should it become necessary to do so.'

Harry opened a pixel-blurred mouth and laughed. 'In case of emergency, break laws of physics.'

'Start working on it, Harry,' Michael said wearily. 'Shira, it’s not impossible. Wormholes are inherently unstable. Active feedback has to be built into the design, to enable a hole to endure…'

But Shira had turned away again and was bent over her data. In the semidarkness of the lifedome, with her face lit from beneath by the pink-blue glow of Poole’s old data, her eyes were huge and liquid.

She was shutting them out once more.

'If only the Friends would let us in on their secret,' Michael said, half to himself. 'Then perhaps we could assess the risks, analyze the potential benefits against the likely costs of allowing them to go ahead.'

'But they won’t,' Harry said. 'All they’ll tell us is how the Project will make it all right in the end.'

'Yes,' Parz said. 'One senses from their words that it is as if the Project will not merely justify any means, any sacrifice — but will somehow nullify the sacrifice itself, in its unraveling.' He looked at Michael. 'Is that possible?'

Michael sighed, feeling very tired, very old; the weight of centuries pressed down on him, evidently unnoticed by the Virtual copy of his father, by this faded bureaucrat, by the baffling, enigmatic girl from fifteen centuries away. 'If they won’t tell us what they’re up to, maybe we can try to work it out. We know that the core of the Project is the implosion, the induced gravitational collapse of Jupiter, by the implanting of seed singularities.'

'Yes,' Parz said. 'But there is a subtle design. We know already that the precise form of that collapse — the parameters of the resulting singularity — is vital to the success of the Project. And that’s what they hoped to engineer with their singularity bullets.'

Harry frowned hugely. 'What’s the point? One singularity is much like another. Isn’t it? I mean, a black hole is black.'

Michael shook his head. 'Harry, a lot of information gets lost, destroyed, when a black hole forms from a collapsing object. A black hole forming is like an irruption of increased entropy into the universe. But there are still three distinguishing quantities associated with any hole: its mass, its electrical charge, and its spin.'

A nonrotating, electrically neutral hole, Michael said, would have a spherical event horizon — the Schwarzchild solution to Einstein’s ancient, durable equations of general relativity. But a rotating, charged object left behind a Kerr-Newman hole: a more general solution to the equations, a nonspherical horizon.

Parz was performing gentle, weightless somersaults; he looked like a small, sleek animal. 'Kerr-Newman predicts that if one may choose mass, charge, and spin, one may sculpt event horizons.'

Harry smiled slowly. 'So you can customize a hole. But my question still stands: so what?'

'One could go further,' Parz said, still languidly somersaulting. 'One could construct a naked singularity.'

'A naked singularity?'

Michael sighed. 'All right, Harry. Think of the formation of a hole again: the implosion of a massive object, the formation of an event horizon.

'But, within the event horizon, the story isn’t over yet. The matter of the dead star keeps imploding; nothing — not pressure from the heat of the core, not even the Pauli exclusion principle — can keep it from collapsing all the way.'

Harry frowned. 'All the way to what?'

'A singularity. A flaw in spacetime; a place where spacetime quantities — mass/energy density, space curvature — all go off the scale, to infinity. Inside a well-behaved black hole, the singularity is effectively cloaked from the rest of the universe by the event horizon. The horizon renders us safe from the damage the singularity can do. But there are ways for singularities to form without a cloaking event horizon — to be ‘naked.’ If a star is spinning rapidly enough before its collapse, for instance… Or if the mass distribution is not compact enough in the first place — if it is elongated, or spiky—'

The singularity in such a solution wouldn’t be a point, as would form at the center of a spherically symmetric, nonrotating star. Instead, the material of the star would collapse to a thin disk — like a pancake — and the singularity would form within the pancake, and along a spike through the axis of the pancake — a spindle of flawed spacetime.

The naked singularity would be unstable, probably — it would rapidly collapse within an event horizon — but it would last long enough to do a lot of damage -

Harry frowned. 'I don’t like the sound of that. What damage?'

Poole locked his hands behind his head. 'How can I explain this? Harry, it’s all to do with boundary conditions…'

* * *

Spacetime could only evolve in an orderly and predictable way if its boundaries, in space and time, were themselves orderly. The boundaries had to satisfy criteria of regularity called Cauchy conditions; causality itself could only flow from stable Cauchy boundaries.

There were three types of boundary. In the beginning there was the initial singularity — the Big Bang, from which the universe expanded. That was one boundary: the start of time.

Then there were boundaries at infinity. Spacelike infinity contained all the places infinitely remote from the observer… and there was a boundary far upwhen, at timelike infinity. At the end of all world lines.

The initial singularity, and the boundaries at spacelike and timelike infinity, were all Cauchy boundaries…

But there was a third class of boundary.

Naked singularities.