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Quantum gravity predictions for black hole interior geometry

机译:黑洞内部几何形状的量子引力预测

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In a previous work we derived an effective Hamiltonian constraint for the Schwarzschild geometry starting from the full loop quantum gravity Hamiltonian constraint and computing its expectation value on coherent states sharply peaked around a spherically symmetric geometry. We now use this effective Hamiltonian to study the interior region of a Schwarzschild black hole, where a homogeneous foliation is available. Descending from the full theory, our effective Hamiltonian, though still bearing the well known ambiguities of the quantum Hamiltonian operator, preserves all relevant information about the fundamental discreteness of quantum space. This allows us to have a uniform treatment for all quantum gravity holonomy corrections to spatially homogeneous geometries, unlike the minisuperspace loop quantization models in which the effective Hamiltonian is postulated. We show how, for several geometrically and physically well motivated choices of coherent states, the classical black hole singularity is replaced by a homogeneous expanding Universe. The resultant geometries have no significant deviations from the classical Schwarzschild geometry in the pre-bounce sub-Planckian curvature regime, evidencing the fact that large quantum effects are avoided in these models. In all cases, we find no evidence of a white hole horizon formation. However, various aspects of the post-bounce effective geometry depend on the choice of quantum states.
机译:在先前的工作中,我们从全环量子引力哈密顿约束出发,并针对球对称几何周围急剧峰值的相干态计算了其期望值,从而得出了Schwarzschild几何的有效哈密顿约束。现在,我们使用这种有效的哈密顿量来研究Schwarzschild黑洞的内部区域,在该区域中可以使用均质的叶面。从完整的理论出发,我们有效的哈密顿量,尽管仍然带有量子哈密顿量算子的众所周知的歧义,但保留了有关量子空间基本离散性的所有相关信息。这使我们能够对所有对量子均一性校正到空间上均一的几何形状进行统一处理,这与其中假设有效哈密顿量的微型超空间环路量化模型不同。我们展示了如何针对几种几何和物理上具有良好动机的相干态选择,用均匀扩展的Universe代替经典的黑洞奇点。最终的几何形状在反弹前的子普朗克曲率范围内与经典的Schwarzschild几何形状没有显着偏差,证明了在这些模型中避免了大量子效应的事实。在所有情况下,我们都没有发现白洞地平线形成的证据。但是,反弹后有效几何形状的各个方面取决于量子态的选择。

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