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arXiv 2311.02585gr-qchep-thmath-phmath.MP
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广义相对论中量子修正塌缩恒星的命运

The fate of a Quantum-Corrected Collapsing Star in General Relativity

Shibendu Gupta Choudhury, Soumya Chakrabarti

AI总结:

本研究将圈量子引力修正引入引力塌缩模型,发现临界参数λ决定最终命运:λ>0产生非奇异虫洞,λ<0可能形成三视界包裹的奇点,并伴随能量条件违反。

摘要:

我们将圈量子引力启发的一些修正引入引力塌缩的概念中,并提出了一个完整的动力学过程模型。该模型承载了曲率标量的质量无关上限的本质,这一上限最初被发现是圈量子引力中黑洞的一个关键特征。量子启发的内部区域浸没在充满零辐射的几何中,它们在一个独特的边界超曲面上进行匹配。该过程的最终命运取决于度规张量系数的不均匀性。我们发现了嵌入在内部度规共形因子不均匀性中的一个临界参数λ。λ<0的示例强制最终塌缩至奇点,而λ>0的情况产生非奇异塌缩,导致一个模共形因子的圈量子修正史瓦西几何。有趣的是,对于λ<0的情况,也存在量子效应能够引起反弹但不足以阻止最终奇点形成的情形。我们研究了λ<0情况下的陷获面形成条件,以推断最终奇点的可见性。有趣的是,我们发现塌缩过程中可能形成三个视界。最终它们全部合并为一个单一视界,包裹住最终奇点。对于非奇异情况,球体有可能演化成一个虫洞喉,其半径被发现与临界参数λ成反比。根据演化的性质和壳层区域,塌缩壳层违反了一些标准能量条件,这些条件可以与量子启发的修正相关联。

英文摘要:

We incorporate some corrections inspired by loop quantum gravity into the concept of gravitational collapse and propose a complete model of the dynamic process. The model carries the essence of a mass-independent upper bound on the curvature scalars originally found as a crucial feature of black holes in loop quantum gravity. The quantum-inspired interior is immersed in a geometry filled with null radiation and they are matched at a distinct boundary hypersurface. The ultimate fate of the process depends on inhomogeneities of the metric tensor cofficients. We find a critical parameter $λ$ embedded in the inhomogeneity of the conformal factor of the interior metric. Examples with $λ< 0$ enforce an eventual collapse to singularity and $λ> 0$ cases produce a non-singular collapse resulting in a loop-quantum-corrected Schwarzschild geometry modulo a conformal factor. Interestingly, for $λ< 0$ as well, there exist situations where the quantum effects are able to cause a bounce but fall short of preventing the ultimate formation of singularity. The trapped surface formation condition is studied for $λ<0$ case to infer about the visibility of the final singularity. Interestingly, we find a possibility of formation of three horizons during the course of the collapse. Eventually all of them merge into one single horizon which envelopes the final singularity. For the non-singular case, there is a possibility that the sphere can evolve into a wormhole throat whose radius is found to be inversely proportional to the critical parameter $λ$. Depending on the nature of evolution and the shell regions, the collapsing shells violate some standard energy conditions which can be associated with the quantum inspired corrections.

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