Define the Schwarzschild radius and give its approximate expression in terms of mass.

• A. The Schwarzschild radius is the radius of the event horizon of a non-rotating black hole; R_s = 2GM/c^2.
• B. R_s is the radius of the accretion disk's inner edge for rotating black holes.
• C. R_s is the radius of the black hole's singularity.
• D. R_s is the distance light travels in one year around the black hole.

Answer: (A)

The Schwarzschild radius is the radius of the event horizon for a non-rotating black hole. It represents the boundary where the escape velocity equals the speed of light, so nothing inside can escape to the outside universe. Its approximate expression in terms of mass is R_s = 2GM/c^2, where G is Newton’s constant and c is the speed of light. In practical units, this becomes about 2.95 kilometers times the black hole’s mass in solar masses (R_s ≈ 2.95 km × (M/M_sun)). This means more massive black holes have larger horizons, but the radius scales linearly with mass.

It’s not the radius of the black hole’s singularity (the singularity is at r = 0 in the Schwarzschild solution), nor the inner edge of an accretion disk for rotating black holes (that geometry is more complex in Kerr black holes), and it isn’t related to a distance light travels in a year (that would be a light-year, a different concept).