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A black hole you could drive across in under an hour, and that the whole Vigil circles at a distance.
How big is a black hole of this mass?
Vesper has 12 solar masses and spins at 0.70 of the maximum physics. Its horizon has a radius of 30.4 km, so the hole is 61 km across. At 70 km/h you would need about 52 minutes to drive across it, if there were anything to drive on.
The horizon is far from the only thing that matters. Light that passes within 92 km of the centre is captured, and the photon sphere sits at 53 km without spin. From 100,000 km away the shadow is only 6.3 arcminutes wide, but the stars behind it are bent into a ring 3.1 degrees across.
What does it do there, and why is it the centre?
Vesper is the Vigil's power station of the far future. In 2540 Ember's light runs the plant, and the hole carries it only after Ember dies simulation. Gas that falls toward a spinning hole can circle as close as 3.4 gravitational radii, the innermost stable orbit, and on the way down about 10.4 percent of its rest-mass energy is radiated as light physics. Hydrogen fusion releases far less of its fuel's rest-mass energy. The feeding happens in the Engine, and the seed chose this system for it.
Vesper is cold. Its Hawking temperature is 4.3 nanokelvin, colder than the 2.7 K sky, so it absorbs more than it emits physics. That makes it a tempting place to dump waste heat, and it does not work: the capture area is small, and at most 4.9 × 109 W of 30 K glow can fall in.
Its horizon could hold up to 1.9 × 1079 bits frontier. Physicists still argue whether that count describes anything a computer could use.
Close in, nothing human-sized survives. The tide across a two-metre body at the horizon is 1.5 × 107 times the pull of gravity at Earth's surface physics. A housed mind in a probe can orbit, and cannot hover.
What does it teach?
How a horizon and its shadow work is in What is a black hole? and Why the hole looks like that. Why the tide kills long before the horizon is in Ships die of tides, not of curvature. The rest-mass-energy-to-radiation trade is in Feeding a black hole, and its limit on the heat dump is in The black hole is not your freezer. Vesper's spin stores a fraction 0.074 of its mass-energy as rotational energy, which Mining a spinning hole explains physics.