发表机构
Ruprecht-Karls-Universität（鲁普雷希特·卡尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
通过量子化旋转参数相等的奇数维Kerr-AdS黑洞外部区域，利用时间与空间本征函数乘积求解，并采用与内部区域一致的最大重数，实现内外区域酉等价，从而在量子层面消除信息悖论。
AI 中文摘要
我们使用我们的量子引力模型，对旋转参数全部相等的奇数维Kerr-AdS黑洞的外部区域进行量子化。由此得到的双曲方程通过时间本征函数$w_i$与空间本征分布$v_{ij}$的乘积来求解，其中时间本征函数$w_i$对应的所有本征值重数均为1，而空间本征分布$v_{ij}$对应于相同的本征值但重数$m_i\ge 1$。原则上，$m_i$可以任意大。当仅考虑外部区域时，没有确定$m_i$值的判据。然而，当同时考虑内部区域的量子化时，这种模糊性不会出现，因为可以选择最大重数。因此，在外部区域使用相同的值是自然的。由于时间哈密顿量在两个区域中相同，内部和外部本征值一致，这一选择定义了相应希尔伯特空间与哈密顿量之间的酉等价。希尔伯特空间及其各自哈密顿量之间的酉等价保留了黑洞内部和外部区域所有正常态所携带的完整量子统计信息。因此，在量子层面不存在信息悖论。
英文摘要
We quantize the exterior region of an odd-dimensional Kerr-AdS black hole, in which all rotational parameters are equal, using our model of quantum gravity. The resulting hyperbolic equation is solved by products of temporal eigenfunctions $w_i$, whose corresponding eigenvalues all have multiplicity one, and spatial eigendistributions $v_{ij}$ corresponding to the same eigenvalues but having multiplicities $m_i\ge 1$. In principle, the $m_i$ may be arbitrarily large. When only the exterior region is considered, there is no criterion for determining the values of the $m_i$. However, when the quantization of the interior region is also considered, the same ambiguity does not arise, because the multiplicities can be chosen to be maximal. It is therefore natural to use the same values in the exterior region. Because the temporal Hamiltonian is the same in both regions, the interior and exterior eigenvalues coincide, and this choice defines a unitary equivalence between the respective Hilbert spaces and Hamiltonians. The unitary equivalence between the Hilbert spaces and their respective Hamiltonians preserves the complete quantum-statistical information carried by all normal states in the interior and exterior regions of the black hole. Hence, there is no information paradox at the quantum level.
Comments33 pages
Journal refSymmetry 18, no. 10, 1627 (2026)
