Quantum effects are studied in both Schwarzschild spacetime and a spacetime in which a null shell collapses to form a black hole via the vacuum polarization $⟨{\varphi }^2⟩$ and stress-energy tensor $⟨T_{ab}⟩$ for a massless minimally coupled scalar field in two dimensions. For Schwarzschild spacetime, the focus is on the Boulware and Unruh states. For the collapsing null shell spacetime, the in vacuum state is used. Instabilities of the Unruh and in states resulting from the behavior of $⟨{\varphi }^2⟩$ in the regions inside and outside of the horizon are found. The question of how well the Unruh state for the eternal black hole approximates quantum effects in the interior of a black hole that forms from collapse is addressed.

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• Quantum aspects of black holes
• Quantum fields in curved spacetime