Recently, it was shown that, in an effective description motivated by loop quantum gravity, singularities of the Kruskal spacetime are naturally resolved [A. Ashtekar, J. Olmedo and P. Singh, Phys. Rev. Lett. 121 (2018) 241301; A. Ashtekar, J. Olmedo and P. Singh, Phys. Rev. D 98 (2018) 126003]. In this paper, we explore a few properties of this quantum corrected effective metric. In particular, we (i) calculate the Hawking temperature associated with the horizon of the effective geometry and show that the quantum correction to the temperature is completely negligible for macroscopic black holes, just as one would hope; (ii) discuss the subtleties associated with the asymptotic properties of the spacetime metric, and show that the metric is asymptotically flat in a precise sense; (iii) analyze the asymptotic fall-off of curvature; and, (iv) show that the ADM energy is well defined (and agrees with that determined by the horizon area), even though the curvature falls off less rapidly than in the standard asymptotically flat context.

中文翻译：

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克鲁斯卡尔几何最近量子扩展的性质

最近，研究表明，在环量子引力的有效描述中，克鲁斯卡尔时空的奇点自然得到解决 [A. Ashtekar，J. Olmedo 和 P. Singh，Phys。牧师莱特。121（2018）241301；A. Ashtekar、J. Olmedo 和 P. Singh，Phys。修订版 D 98 (2018) 126003]。在本文中，我们探讨了这种量子校正有效度量的一些特性。特别是，我们 (i) 计算了与有效几何视界相关的霍金温度，并表明对于宏观黑洞，温度的量子校正完全可以忽略不计，正如人们所希望的那样；(ii) 讨论与时空度量的渐近特性相关的微妙之处，并表明该度量在精确意义上是渐近平坦的；(iii) 分析曲率的渐近衰减；和，