Which theorem states that black holes can be characterized solely by mass, charge, and angular momentum?

• A. Poynting theorem
• B. Noether's theorem
• C. Gauss's law
• D. No-hair theorem

Answer: (D)

The key idea being tested is that, in classical general relativity, a black hole is fully described by just three externally observable quantities: mass, electric charge, and angular momentum. This is captured by the no-hair theorem, which says that all other details about the matter that formed the black hole or any surrounding fields are not observable from outside the event horizon. The exterior spacetime of a stationary black hole collapses to one of a few canonical solutions— Kerr for a rotating uncharged hole, Reissner-Nordström for a non-rotating charged hole, or Kerr-Newman for a charged rotating hole—each described entirely by those three parameters. Because of this, black holes have “no hair”—no additional distinguishing features can influence measurements made outside the horizon. The other ideas mentioned refer to different physics: Poynting’s theorem concerns electromagnetic energy flow, Noether’s theorem connects symmetries to conserved quantities, and Gauss’s law relates electric flux to charge—none of which state that black holes are classified solely by mass, charge, and angular momentum.