Which statement correctly distinguishes the event horizon from the apparent horizon in black hole spacetimes?

• A. The apparent horizon is a global boundary that defines escape; the event horizon is a locally defined surface.
• B. The event horizon is a local property that depends on the observer’s frame.
• C. They are always identical.
• D. The apparent horizon exists only in Newtonian spacetimes.

Answer: (C)

The key idea here is that horizons in black hole spacetimes come in two different flavors: a global boundary and a local, slice-dependent surface. The event horizon is the global boundary of no return: it’s defined by the behavior of light rays over the entire future of the spacetime. In contrast, the apparent horizon is a locally defined surface on a particular time slice where the outward expansion of light rays vanishes; it’s a marginally outer trapped surface and depends on the chosen slice.

In a stationary spacetime like Schwarzschild, the geometry doesn’t change with time, so the surface you’d identify as the event horizon also happens to be the apparent horizon. They coincide there. But in dynamical situations—when the black hole is evolving due to accretion, mergers, or other changes—the two horizons generally do not match. The apparent horizon stays as a locally defined boundary on the current slice and can move or even appear/vanish as matter evolves, while the event horizon’s position depends on the entire future evolution and typically lies outside the instantaneous apparent horizon.

That’s why the statement that they are always identical isn’t generally true. The other options misstate which horizon is global versus local, or claim a relationship that isn’t universally valid (and the notion that the apparent horizon exists only in Newtonian spacetimes is simply incorrect).