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The Hartle–Hawking–Israel state on spacetimes with stationary bifurcate Killing horizons
Reviews in Mathematical Physics ( IF 1.8 ) Pub Date : 2021-06-15 , DOI: 10.1142/s0129055x21500288
Christian Gérard 1
Affiliation  

We consider a free massive quantized Klein–Gordon field in a spacetime (M,g) containing a stationary bifurcate Killing horizon, i.e. a bifurcate Killing horizon whose Killing vector field is globally time-like in the right wedge + associated to the horizon. We prove the existence of the Hartle–Hawking–Israel (HHI) vacuum state, which is a pure state on the whole spacetime whose restriction to + is a thermal state ωTH for the time-like Killing field at Hawking temperature TH = κ(2π)1, where κ is the surface gravity of the horizon. We show that the HHI state is a Hadamard state and is the unique Hadamard state which is equal to the double TH1-KMS state in the double wedge +. We construct the HHI state by Wick rotation in Killing time coordinates, using the notion of the Calderón projector for elliptic boundary value problems.

中文翻译:

时空上的哈特尔-霍金-以色列状态具有静止的分叉杀死视界

我们考虑时空中的一个自由大质量量化的 Klein-Gordon 场(,G)包含一个固定的分叉 Killing 视界,即一个分叉的 Killing 视界,其 Killing 向量场在右楔中是全局时间类的+与地平线相关联。我们证明了哈特尔-霍金-以色列(HHI)真空态的存在,它是整个时空中的一个纯态,其限制为+是热态ωH霍金温度下的类时间杀戮场H = κ(2π)-1, 在哪里κ是地平线的表面重力。我们证明了 HHI 状态是一个 Hadamard 状态并且是唯一的 Hadamard 状态,它等于双H-1-双楔中的KMS状态-+. 我们通过在 Killing 时间坐标中的 Wick 旋转构建 HHI 状态,使用 Calderón 投影仪的概念来解决椭圆边值问题。
更新日期:2021-06-15
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