旋转吸积黑洞内视界$\langleϕ^2\rangle$的重整化
Renormalization of $\langleϕ^2\rangle$ at the inner horizon of rotating, accreting black holes
摘要：
在经典理论中，受扰动的旋转黑洞的内视界会经历一种被称为质量暴胀的不稳定性，其中时空曲率会由于超相对论性的交叉辐射流而发散。这种不稳定性的一般结果目前被认为是一个强大的类空奇点，可能与一个弱的零奇点一起幸存下来。然而，对于一个现实的黑洞时空，在这种情况下的量子反作用还没有完全计算出来。在这里，我们考虑一个无质量的量子化标量场$ϕ$的膨胀卡斯纳时空，最近开发的模型的内视界几何的旋转，吸积黑洞。有了这个时空，我们使用数值绝热正则化来计算$\langleϕ^2\rangle_\text{ren}$，两点关联函数的重正化符合极限，作为量子应力-能量张量行为的指针。$\langleϕ^2\rangle_\text{ren}$一般被发现是非零的内视界附近，发散的曲率经典发散，和较小的黑洞自旋或吸积率较大。
英文摘要：
Classically, the inner horizon of a perturbed, rotating black hole undergoes an instability known as mass inflation, wherein the spacetime curvature diverges as a result of hyper-relativistic crossing streams of ingoing and outgoing radiation. The generic outcome of this instability is currently believed to be a strong, spacelike singularity, potentially alongside a weak, null singularity surviving at late times. However, the quantum back-reaction in this regime has yet to be fully calculated for a realistic black hole spacetime. Here we consider a massless quantized scalar field $ϕ$ over the inflationary Kasner spacetime, a recently developed model for the inner horizon geometry of a rotating, accreting black hole. With this spacetime, we use numerical adiabatic regularization to calculate $\langleϕ^2\rangle_\text{ren}$, the renormalized coincidence limit of the two-point correlation function, as a pointer to the behavior of the quantum stress-energy tensor. $\langleϕ^2\rangle_\text{ren}$ is generically found to be nonzero near the inner horizon, divergent where the curvature classically diverges, and larger for smaller black hole spins or accretion rates.
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