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arXiv 1010.3767gr-qchep-th
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Einstein-Rosen虫洞喉道的量子动力学

Quantum dynamics of the Einstein-Rosen wormhole throat

Gabor Kunstatter, Jorma Louko, Ari Peltola

摘要:

我们考虑了永久史瓦西黑洞的爱因斯坦虫孔喉理论的聚合物量子化。我们数值求解差分方程描述的量子演化的初始高斯,半经典波包。正如先前对圈量子宇宙学的研究所预期的那样,波包保持半经典状态,直到它接近经典奇点,在经典奇点处它进入量子状态,波动变大。当波包从原点反射并在后期形成近高斯但不对称的半经典态时,半径的期望值达到最小值。最小值以非平凡的方式取决于脉冲的初始质量/能量、其宽度和聚合规模。当波包在反弹点附近足够窄时,得到了半经典反弹半径。虽然数字变得难以控制,在这个限制,我们认为,脉冲的有限宽度的反弹持续聚合规模为零,这表明在这个模型中的环量子引力效应模仿聚合物量子化不发挥关键作用的量子反弹。

英文摘要:

We consider the polymer quantization of the Einstein wormhole throat theory for an eternal Schwarzschild black hole. We numerically solve the difference equation describing the quantum evolution of an initially Gaussian, semi-classical wave packet. As expected from previous work on loop quantum cosmology, the wave packet remains semi-classical until it nears the classical singularity at which point it enters a quantum regime in which the fluctuations become large. The expectation value of the radius reaches a minimum as the wave packet is reflected from the origin and emerges to form a near Gaussian but asymmetrical semi-classical state at late times. The value of the minimum depends in a non-trivial way on the initial mass/energy of the pulse, its width and the polymerization scale. For wave packets that are sufficiently narrow near the bounce, the semi-classical bounce radius is obtained. Although the numerics become difficult to control in this limit, we argue that for pulses of finite width the bounce persists as the polymerization scale goes to zero, suggesting that in this model the loop quantum gravity effects mimicked by polymer quantization do not play a crucial role in the quantum bounce.

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