A stellar-mass black hole accretes 1 kg of hydrogen. Compared to a nuclear fusion reactor that burns the same 1 kg of hydrogen, the accreting black hole radiates approximately:
AAbout the same amount of energy — both processes release energy by converting mass
BAbout 10 times less energy — accretion is less efficient than the strong nuclear force driving fusion
CBetween 10 and 60 times more energy — accretion efficiency (6–42%) greatly exceeds nuclear fusion efficiency (~0.7%)
DNearly all of the rest-mass energy — black holes convert matter to pure radiation with near-100% efficiency
Nuclear fusion converts only about 0.7% of rest-mass energy to radiation (the mass difference between reactants and products). Accretion onto a non-spinning black hole converts ~6%, and onto a maximally spinning Kerr black hole ~42%. This 10–60× advantage is why accreting black holes are the most luminous sustained energy sources in the universe — quasars can outshine entire galaxies. Option D confuses accretion with matter-antimatter annihilation (100% efficient) — accretion doesn't destroy the infalling matter, it liberates gravitational potential energy as it spirals inward.
Question 2 Multiple Choice
Why does infalling material form a disk around a black hole rather than falling straight in?
AMagnetic fields emanating from the black hole deflect infalling material into an orbital plane
BAny infalling material with even slight sideways motion carries angular momentum, causing it to orbit rather than plunge directly inward
CGas pressure from already-present disk material forces new infalling gas to align with the disk plane
DRadiation pressure from the hot inner disk repels material before it can fall radially inward
Angular momentum conservation is the fundamental reason. Any gas cloud with even a tiny rotation — which all real gas has, due to turbulence, galactic shear, or orbital motion — carries angular momentum. Infalling material must conserve this angular momentum, so it cannot fall straight in; it circularizes into an orbit. Material from different distances orbits at different speeds (inner orbits faster, like Kepler's laws), creating shearing between adjacent layers. This differential rotation drives friction that heats the disk and allows matter to slowly lose angular momentum and spiral inward.
Question 3 True / False
The innermost stable circular orbit (ISCO) is smaller for a rapidly spinning Kerr black hole than for a non-spinning Schwarzschild black hole, which is why spinning black holes achieve higher accretion efficiencies.
TTrue
FFalse
Answer: True
The ISCO is the smallest radius at which stable circular orbits exist. For a Schwarzschild (non-spinning) black hole, the ISCO is at 3 Schwarzschild radii (6GM/c²). For a maximally spinning Kerr black hole, the ISCO for prograde orbits shrinks to 0.5 Schwarzschild radii — much closer to the event horizon. Matter that reaches the ISCO and plunges inward from this final orbit releases gravitational energy proportional to how deep in the potential well the ISCO sits. A smaller ISCO means deeper in the potential well, meaning more gravitational energy converted to radiation before the matter crosses the event horizon. This is why spin dramatically increases accretion efficiency from ~6% to ~42%.
Question 4 True / False
Accretion onto a black hole is less efficient than nuclear fusion in stars because the event horizon swallows much of the radiation produced in the inner disk before it can escape to observers.
TTrue
FFalse
Answer: False
This reverses the actual efficiency comparison. Accretion converts 6–42% of rest-mass energy to radiation, while nuclear fusion converts only ~0.7%. The key is that the radiation is produced in the accretion disk, which extends well outside the event horizon — the innermost disk regions are still at radii of several to tens of gravitational radii. Most radiation escapes to infinity before the matter crosses the event horizon. Some fraction of energy does fall in with the accreting matter, and thin disk theory accounts for this, but the net radiative efficiency is still far higher than nuclear fusion.
Question 5 Short Answer
Explain why angular momentum is the central physical problem in black hole accretion, and how the accretion disk solves this problem to allow matter to spiral inward.
Think about your answer, then reveal below.
Model answer: Angular momentum is conserved, so infalling matter cannot simply drop into a black hole — it must orbit. The problem is that matter needs to lose angular momentum to move inward (lower orbits have less angular momentum for a given mass). The accretion disk solves this through viscosity: friction between adjacent disk annuli moving at slightly different orbital speeds acts as a torque, transferring angular momentum outward through the disk while allowing matter to sink inward. This viscous transport is both the problem's solution and the energy source: the friction that transports angular momentum also converts orbital kinetic energy to heat, radiating that energy as the disk luminosity. Without a mechanism to shed angular momentum, matter would orbit forever and never accrete.
The nature of the viscosity is itself a deep unsolved problem — molecular viscosity is far too weak. The current leading explanation is the magnetorotational instability (MRI), where a weak magnetic field threaded through a differentially rotating disk becomes unstable and generates MHD turbulence that acts as an effective viscosity. The MRI provides the angular momentum transport that makes accretion physically possible at the luminosities observed.