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arXiv 2110.03069gr-qc
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彩虹黑洞的量子引力坍缩

Rainbow Black Hole From Quantum Gravitational Collapse

Aliasghar Parvizi, Tomasz Pawłowski, Yaser Tavakoli, Jerzy Lewandowski

摘要:

在坍缩均匀尘埃球的量子时空上传播的标量场模式的量子演化被有效地写成相同量子模式在(半经典)缀饰几何上的演化。当场的反作用被丢弃时,经典时空奇异性由于量子引力效应而被解决,并被在修饰的塌缩背景上的量子反弹所取代。在存在反作用的情况下,出射(内部)修饰的几何形状变得依赖于模式,并且与每个模式的反作用相关联的能量密度作为辐射流体缩放。分析了这种所谓的{ \em彩虹}修饰背景的半经典动力学。事实证明,与仅存在尘埃流体的情况相比,反向反应效应加速了反弹的发生。通过匹配尘埃边界的内部和外部区域,一个依赖于模式的黑洞几何出现作为外部时空。讨论了这种彩虹黑洞的性质。特别地,该模式依赖性导致引力透镜过程中的色差,其最大幅度通过计算所谓的爱因斯坦角来估计。

英文摘要:

Quantum evolution of a scalar field's modes propagating on quantum spacetime of a collapsing homogeneous dust ball is written effectively, as an evolution of the same quantum modes on a (semiclassical) dressed geometry. When the backreaction of the field is discarded, the classical spacetime singularity is resolved due to quantum gravity effects and is replaced by a quantum bounce on the dressed collapse background. In the presence of backreaction, the emergent (interior) dressed geometry becomes mode dependent and the energy density associated with the backreaction of each mode scales as a radiation fluid. Semiclassical dynamics of this so-called {\em rainbow} dressed background is analyzed. It turns out that the backreaction effects speed up the occurrence of the bounce in comparison to the case where only a dust fluid is present. By matching the interior and exterior regions at the boundary of dust, a mode-dependent black hole geometry emerges as the exterior spacetime. Properties of such a rainbow black hole are discussed. That mode dependence causes, in particular, a chromatic aberration in the gravitational lensing process of which maximal magnitude is estimated via calculation of the so-called Einstein angle.

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