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Effective quantum dust collapse via surface matching
Classical and Quantum Gravity ( IF 3.5 ) Pub Date : 2021-08-13 , DOI: 10.1088/1361-6382/ac103e
Johannes Münch

The fate ofmatter forming a black hole isstill an open problem, althoughmodels of quantumgravity corrected black holes are available. In loop quantumgravity (LQG)models were presented, which resolve the classicalsingularity in the centre of the black hole bymeans of a black-to-white hole transition, butneglect the collapse process.Thesituation issimilar in other quantumgravity approaches, where eternalnon-singularmodels are available. In this paper, astrategy is presented to generalise these eternalmodels to dynamical collapsemodels bysurfacematching.Assuming (1) the validity of astatic quantum black holespacetime outside the collapsingmatter, (2) homogeneity of the collapsingmatter, and (3) differentiability at thesurface of thematter fixes the dynamics of thespacetime uniquely. It is argued that these assumptions resemble a collapse of pressure-less dust and thusgeneralises the Oppenheimer–Snyder–Dattmodel, althoughno precisemodel of thematterhas to be assumed. Hawkingradiation issystematicallyneglected in this approach.The junction conditions and thespacetime dynamics are discussedgenerically for bouncing black holespacetimes, as proposed by LQG, although thescheme is approachindependent. Further, the equations are explicitlysolved for the recentmodel Bodendorfer et al (2019 Class. Quantum Grav. 36 195015) and aglobalspacetime picture of the collapse is achieved.The causalstructure is discussed in detail and the Penrose diagram is constructed.The trajectory of the collapsingmatter is completely constructed from an inside and outside observer point of view.Thegeneral analysisshows that thematter is collapsing and re-expanding and crosses the Penrose diagram diagonally.This way the infinite tower of Penrose diagrams, as proposed byseveral LQGmodels, isgenericallynot cut out. Questions about different timescales of the collapse for in- and outside observers can be answered.



中文翻译:

通过表面匹配有效的量子尘埃坍塌

形成黑洞的物质的命运仍然是一个悬而未决的问题,尽管可以使用量子引力校正黑洞的模型。提出了环内量子引力 (LQG) 模型,它通过黑洞到白洞的跃迁解决了黑洞中心的经典奇异性,但忽略了坍缩过程。 这种情况与其他量子引力方法类似,其中有永恒的非奇异模型. 在本文中,提出了通过表面匹配将这些永恒模型推广到动力学坍缩模型的策略。时空动力学独一无二。有人认为,这些假设类似于无压力尘埃的坍塌,因此概括了奥本海默 - 斯奈德 - 达特模型,尽管没有对该问题的精确模型进行假设。在这种方法中,霍金辐射被系统地忽略了。虽然该方案是方法独立的,但正如 LQG 提出的那样,一般讨论了用于反弹黑洞时空的结条件和时空动力学。此外,方程是为最近的模型 Bodendorfer 显式求解的et al (2019 Class. Quantum Grav . 36 195015) 并获得了坍缩的全局时空图。详细讨论了因果结构并构建了彭罗斯图。坍缩物质的轨迹完全是从内部和外部观察点构建的视图。一般分析表明,物质正在折叠和重新膨胀,并与彭罗斯图对角线交叉。这样,由几个 LQG 模型提出的彭罗斯图的无限塔一般不会被剪掉。可以回答关于内部和外部观察者崩溃的不同时间尺度的问题。

更新日期:2021-08-13
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