Quantum Effects in the Interior of a Black Hole

The interiors of black holes provide a convenient space for exploring quantum effects because the curvature of spacetime becomes infinite at the central singularity. We consider a massless, minimally coupled, scalar quantum field φ, which can be thought of as a simple model for the electromagnetic field. We work with eternal black holes in two dimensions and consider two important states: the Boulware, or vacuum state, and the Unruh state, which describes black hole evaporation. To analyze the quantum effects, we calculate the expectation value of the square of the field <φ²>, and the stress-energy tensor of the field. We analyze the behavior of these quantities in the region between the event horizon and the singularity. We also calculate these quantities for a black hole that forms from the collapse of a massless shell of radiation.