The expectation value of the stress-energy tensor \langleT_{\mu\nu}\rangle of a free conformally invariant scalar field is computed in a general static two-dimensional black hole spacetime when the field is in either a zero temperature vacuum state or a thermal state at a nonzero temperature. It is found that for every static two-dimensional black hole the stress-energy diverges strongly on the event horizon unless the field is in a state at the natural black hole temperature which is defined by the surface gravity of the event horizon. This implies that both extreme and nonextreme two-dimensional black holes can only be in equilibrium with radiation at the natural black hole temperature.
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机译:自由共形不变标量场的应力-能量张量\ langleT _ {\ mu \ nu} \ rangle的期望值是在零温度真空状态或零温度真空状态下的一般静态二维黑洞时空中计算的非零温度下的热态。可以发现,对于每个静态二维黑洞,应力场在事件视界上的差异很大,除非该场处于由事件视界的表面重力定义的自然黑洞温度下的状态。这意味着极端和非极端的二维黑洞都只能与自然黑洞温度下的辐射保持平衡。
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