Quantum uncertainty in the area of a black hole

TL;DR

This paper investigates quantum fluctuations of black hole horizons, deriving the variance in their area using linearized quantum gravity, revealing significant quantum uncertainty for large black holes in Planck units.

Contribution

It provides a calculation of horizon area uncertainty in Schwarzschild black holes using the graviton propagator in linearized quantum gravity, highlighting the scale of quantum effects.

Findings

Quantum fluctuations induce large uncertainties in black hole horizon areas.

The standard deviation scales with the product of Schwarzschild radius and Planck length.

Quantum uncertainty becomes significant for macroscopic black holes.

Abstract

Quantum fluctuations of the spacetime metric induce an uncertainty in the horizon area of a black hole. Working in linearized quantum gravity, we derive the variance in the area of a four-dimensional Schwarzschild black hole from the renormalized graviton propagator. We find that the standard deviation of the horizon area scales as the product of the Schwarzschild radius and the Planck length. For macroscopic black holes, the quantum uncertainty is therefore enormous in Planck units.