论文标题
$ \ langleϕ^2 \ rangle $在旋转的内部地平线上的重新归一化，积聚黑洞
Renormalization of $\langleϕ^2\rangle$ at the inner horizon of rotating, accreting black holes
论文作者
论文摘要
从经典上讲，一个扰动的，旋转的黑洞的内部地平线经历了一种被称为质量通胀的不稳定性，其中，由于高偏移性的交叉流和外向辐射的过度交叉流，时空曲率出现了不同。这种不稳定性的通用结果被认为是一种强大的，较强的奇异性，可能与较弱的无效奇异性在后期生存。但是，对于逼真的黑洞时空，该状态的量子反应尚未完全计算。在这里，我们考虑了通货膨胀的Kasner Spacetime上无质量的量化标量场$ ϕ $，这是一个最近开发的模型，用于旋转，积聚黑洞的内部地平线几何形状。使用此时空，我们使用数值绝热正则化来计算$ \ langleϕ^2 \ rangle_ \ text {ren} $，这是两点相关函数的重归于重合限制，作为对量子应力 - 能量张量的行为的指针。 $ \ langleϕ^2 \ rangle_ \ text {ren} $通常在内部地平线附近是非零的，在曲率上有经典的分歧，对于较小的黑洞旋转或积聚率，则较大。
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.
