Quantum Uncertainty of the Horizon Area  

Quantum-gravitational fluctuations of the spacetime metric induce an uncertainty in the horizon area of a black hole. Working in linearized quantum gravity, we’ll derive the variance in the area of a four-dimensional Schwarzschild black hole from the renormalized graviton propagator. Surprisingly, the uncertainty in the area is much larger than the Planck area, scaling instead as the product of the Schwarzschild radius and the Planck length. For a super-massive black hole, the scale of the fluctuations is large enough to make it unclear whether atomic matter could free-fall into a black hole unscathed.