We perform canonical quantization of gravity in the background of a Schwarzschild black hole in the generalized Regge-Wheeler gauge proposed in Kallosh and Rahman [Quantization of gravity in the black hole background, Phys. Rev. D 104, 086008 (2021)]. We find that the Hamiltonian at the quadratic level is unitary and ghost-free. Two canonical degrees of freedom are associated with Zerilli-Moncrief and Cunningham-Price-Moncrief functions of the metric perturbations. The $\ell <2$ part of the Hamiltonian vanishes. This quantization with the unitary Hamiltonian for gravity is valid also in Minkowski space in spherical coordinates.

中文翻译：

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球谐基中重力的量化

我们在 Kallosh 和 Rahman [黑洞背景中的引力量化，Phys. 修订版 D 104 , 086008 (2021)]。我们发现二次水平的哈密顿量是幺正的且没有重影。两个规范的自由度与度量扰动的 Zerilli-Moncrief 和 Cunningham-Price-Moncrief 函数相关联。这$\ell <2$哈密​​顿量的一部分消失。重力的酉哈密顿量的这种量化在球坐标的闵可夫斯基空间中也是有效的。