"Cartan Null? What's wrong with that? Cartan was a great flesher mathematician, who clarified the meaning and consequences of Einstein's work. Null because it's built of null geodesics, the paths followed by light rays."

"Posterity," Prospero declared, "will like it better as `The Falling City' -- its essence unencumbered by your infelicitious words."

Tiet said cooly, "We named this polis after Elie Cartan. Its clone inside Chandrasekhar will be named after Elie Cartan. If you're unwilling to respect that, you might as well head back to Athena right now, because no one here is going to offer you the slightest co-operation."

"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 in falling starlight would be blue-shifted enough to disrupt it, and anything more massive -- like us if we were really here -- would cause chaotic changes even sooner." She instructed the scape to switch to Belinsky-Khalatinikov-Lifshitz geometry, then restarted time.

The two bundles of rays oscillated between circular and elliptical cross-sections as the curvature stretched and squeezed them. Cordelia created a magnifying glass and followed them "in": forwards in time, towards the singularity. She said, "If the orbital periods form a geometric series, there's no limit to the number of orbits you could fit in before the singularity. And the wavelength is blue-shifted in proportion to the size of the orbit, so diffraction effects never take over. So, what's there to stop you doing infinite computation?"