Question

For a non-rotating (Schwarzschild) black hole, how do the sizes of the matter ISCO and the event horizon compare?

a) The matter ISCO is larger
b) They are the same size
c) The event horizon is larger
d) It depends on the black hole's mass

Answer 1

For a Schwarzschild black hole, the matter Innermost Stable Circular Orbit (ISCO) is larger than the event horizon, which is determined by the Schwarzschild radius proportional to the black hole's mass.

Step-by-step explanation:

For a non-rotating (Schwarzschild) black hole, the Innermost Stable Circular Orbit (ISCO) is larger than the event horizon. The ISCO is the closest orbit in which matter can stably orbit a black hole without being dragged inexorably towards the event horizon. The size of the event horizon of a black hole depends on the mass of the black hole, as defined by the Schwarzschild radius (Rs), which is directly proportional to the mass. The formula for the Schwarzschild radius (Rs) indicates that Rs is 3 km times the mass of the black hole in units of the Sun's mass. Thus, since the ISCO is typically a few times larger than Rs, the correct answer to the student's question is: a) The matter ISCO is larger.