Every energy source used by the Vigil can be compared by how much of its fuel's mass-energy it releases as radiation. Burning fuel releases about a ten-billionth of its rest-mass energy. Fusion releases under one percent of the fuel's rest-mass energy. Gas falling into a spinning black hole radiates around a tenth of its rest-mass energy, which is why the Vigil's power station is a black hole rather than a star.
The numbers are small in mass and large in effect. A whole year of the Vigil's first petawatt has a mass equivalent of 350,000 kg. The seed that founded the Vigil moved at a tenth of the speed of light with 4.5 × 1017 joules of kinetic energy, equivalent to the rest-mass energy of 5.0 kg.
Where should I start?
Start with a gram is a fortune. It is the ladder of fuels from chemistry to black holes, and it makes every other page on this site easier. It is also one of the six surprises.
Next, follow the gas into an accretion disk. Feeding a black hole follows the gas as it spirals in, heats up and shines before it falls. The conversion efficiency depends on the hole's spin and the gas flow.
The last step is the spin itself. Mining a spinning hole looks at a black hole as a flywheel: a hole that rotates stores part of its mass-energy as spin energy that can, in principle, be taken out. Vesper is one of those: 0.074 of its total mass-energy, 1.6 × 1047 joules, is stored in its spin, a large reserve relative to the Vigil's power use.
What is it all for?
Power use also creates a cooling requirement. Energy gets turned into computing, and computing gets turned into heat, and the heat has to go somewhere. The heat strand picks up where this one leaves off, and explains why cooling capacity limits the Vigil's computing activity.