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arXiv 2408.01780gr-qchep-th
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带宇宙学常数的对称黑洞-白洞解

Symmetric black-to-white hole solutions with a cosmological constant

Zhong-Wen Feng, Qing-Quan Jiang, Yi Ling, Xiao-Ning Wu, Zhangping Yu

AI总结:

本研究证明哈密顿约束系统动力学不依赖于拉普拉斯函数选择,统一了Rovelli和Ashtekar的黑洞-白洞模型,并通过固定量子参数构造了精确对称及含宇宙学常数的黑洞-白洞解。

摘要:

对于具有哈密顿约束的系统,我们证明其动力学在不同拉普拉斯函数选择下是不变的,无论哈密顿量是否包含量子修正。将此观察应用于黑洞-白洞的内部,我们分析了其在不同拉普拉斯函数选择下的动力学。结果明确表明,Rovelli等人(Class. Quant. Grav. 35, 225003 (2018); Class. Quant. Grav. 35, 215010 (2018))和Ashtekar等人(Phys. Rev. Lett. 121, 241301 (2018); Phys. Rev. D 98, 126003 (2018))提出的两种度规的领头阶展开在过渡面附近表现出相同的行为。因此,在这个意义上,Rovelli等人(Class. Quant. Grav. 35, 225003 (2018); Class. Quant. Grav. 35, 215010 (2018))提出的黑洞-白洞模型可以被解释为圈量子引力框架内解的粗粒化版本。通过在圈量子引力有效理论中适当固定量子参数,构造了黑洞区域和白洞区域之间具有精确对称性的黑洞-白洞解。这种方法规避了可能因黑洞和白洞之间的质量差异而产生的质量放大问题,并提供了一种将微超空间量子化获得的解与协变方法中的解联系起来的方式。最后,构造了带宇宙学常数的黑洞-白洞解。获得了带宇宙学常数的黑洞-白洞内部的数值解,并讨论了其对称行为。

英文摘要:

For a system with a Hamiltonian constraint, we demonstrate that its dynamics is invariant under different choices of the lapse function, regardless of whether the Hamiltonian incorporates quantum corrections. Applying this observation to the interior of black-to-white holes, we analyze its dynamics with different choices of the lapse function. The results explicitly show that the leading-order expansion of both metrics proposed by Rovelli et al. (Class. Quant. Grav. \textbf{35}, 225003 (2018); Class. Quant. Grav. \textbf{35}, 215010 (2018)) and Ashtekar et al. (Phys. Rev. Lett. \textbf{121}, 241301 (2018); Phys. Rev. D \textbf{98}, 126003 (2018)) exhibit identical behavior near the transition surface. Therefore, in this sense the black-to-white hole model proposed by Rovelli et al., (Class. Quant. Grav. \textbf{35}, 225003 (2018); Class. Quant. Grav. \textbf{35}, 215010 (2018)) may be interpreted as a coarse-grained version of the solution within the framework of loop quantum gravity. The black-to-white hole solutions with exact symmetry between the black hole and white hole regions are constructed by appropriately fixing the quantum parameters in the effective theory of loop quantum gravity. This approach circumvents the issue of amplification of mass, which could arise from a mass difference between the black hole and white hole, and provides a way to link the solutions obtained by minisuperspace quantization to those in the covariant approach. Finally, the black-to-white hole solutions with a cosmological constant are constructed. The numerical solutions for the interior of the black-to-white hole with a cosmological constant are obtained, and their symmetric behavior is also discussed.

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