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.

"It sounds fantastic," Harry said.

"Maybe it is. But nobody can think of any reason why such objects shouldn’t form. There are some quite easy ways for this to happen, if you wait long enough. You know that black holes aren’t really ‘black,’ that they have a temperature—"

"Yes. Hawking evaporation. Just like the holes in the earth-craft."

"Small holes like those in the earth-craft’s singularity plane will simply implode when they have evaporated completely. But in the far future, when the singularities at the heart of galaxy-mass holes begin to emerge from within their evaporating horizons -

"Harry, naked singularities are non-Cauchy boundaries to spacetime. There is no order, no pattern to the spacetime that might evolve from a naked singularity; we can’t make any causal predictions about events. Some theorists hold that if a naked singularity were to form, then spacetime — the universe — would simply be destroyed."

"Jesus. Then maybe naked singularities can’t form after all?"

"You should have been a philosopher, Harry."

"I should?"

"That’s the principle of Cosmic Censorship — that there’s something out there, something like the Pauli principle maybe, which would stop the formation of naked flaws. That’s one theory."

"Yeah. But who is this Cosmic Censor? And can we trust him?"

"The trouble is that we can think of too many ways for naked singularities to be formed. And nobody can think of a particularly intelligent mechanism for the Cosmic Censorship to work…"

Parz, hovering, had listened to all this with veined eyelids closed. "Indeed. And perhaps that is the goal of the Friends."

Michael felt the pieces of the puzzle sliding around in his head. "My God," he said softly. "They’ve hinted at a power over history. Do you think they could be so stupid?" He looked up at the Virtual. "Harry, maybe the Friends are trying to change history with a naked singularity…"

"But they could never control it," Parz said, eyes still closed. "It would be utterly random. At best, like lobbing a grenade into a political discussion. It will change the agenda, yes, but in an utterly discontinuous fashion. And at worst—"

"At worst they could wreck spacetime," Michael said.

Harry looked down at him, pixel-blurred, but serious and calm. "What do we do, Michael? Do we help them?"

"Like hell," Michael said quietly. "We have to stop them."

Shira looked up from her data screens, her long neck seeming to uncoil. "You don’t understand," she said calmly. "You’re wrong."