Spherically symmetric contribution to the stress-energy tensor for a quantum field in a collapsing null shell background

The renormalized expectation value of the stress-energy tensor corresponding to a massless minimally-coupled scalar field in the ”in” vacuum state is numerically computed outside the event horizon of a four-dimensional black hole that forms from the collapse of a null shell. The computations are performed in the s-wave sector which is expected to make the largest contribution to the stress-energy tensor. The divergence in the unrenormalized stress-energy tensor is removed by subtracting the unrenormalized expression for the stress-energy

tensor when the field is in the Unruh state. Comparison is made between the components of the renormalized stress-energy tensor in four dimensions and the known results in the two dimensions. The convergence of the stress-energy tensor for the ”in” vacuum state to the stress-energy tensor for the Unruh state at late times is discussed.