Stress-energy tensor for a quantized scalar field when a black hole forms from collapse in four dimensions

The behavior of the stress-energy tensor for a quantized massless minimally coupled scalar field is investigated in a spacetime in which a black hole forms from collapse in four dimensions. The spacetime is a solution to the classical Einstein equations in which a spherically symmetric, null shell collapses to form a black hole. Inside the shell the metric is that of flat space, while outside it is the Schwarzschild metric. The field is in the “in” vacuum state. The difference between the stress-energy tensor for the “in” state and that for the Unruh state in Schwarzschild spacetime is computed in the region outside the shell and outside the event horizon. The Unruh state is the state of the field for Schwarzschild spacetime that describes black hole evaporation. A detailed investigation is made of the approach at late times of the stress-energy tensor for the “in” state to that for the Unruh state.