发表机构
Institut des Hautes Études Scientifiques; International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（高等科学研究所; 理论科学国际中心，塔塔基础研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明量子效应使史瓦西黑洞的静态Love数非零，其大小受普朗克长度平方抑制，源于量子圈图破坏经典偶然对称性。
AI 中文摘要
四维史瓦西黑洞的静态Love数在经典理论中为零。我们证明在量子理论中这一结论并不成立。在世界线有效场论框架下，我们计算了无质量标量粒子和光子在一阶后闵可夫斯基近似下与史瓦西黑洞散射的康普顿振幅的领头阶量子修正，并发现了与静态Love数重整化相关的对数发散。我们得出结论，重整化群跑动必然会产生Love数，其大小被普朗克长度平方与视界半径平方之比（$\ell_{\rm pl}^{2}/r_{\rm h}^{2}$）所抑制。这与经典为零的结论一致，后者是静态广义相对论中偶然对称性的结果，而该对称性被量子圈图所破坏。外推到引力微扰，我们的结果表明史瓦西黑洞的四极静态Love数的大小为 $\lambda \sim M r_{\rm h}^{2} \ell_{\rm pl}^{2}$。
英文摘要
The static Love numbers of four-dimensional Schwarzschild black holes vanish classically. We show that this is not true in the quantum theory. Working in the worldline effective field theory, we compute the leading quantum correction to the Compton amplitude for massless scalars and photons scattering off a Schwarzschild black hole at first post-Minkowskian order, and find logarithmic divergences associated with the renormalization of the static Love numbers. We conclude that renormalization-group running necessarily generates Love numbers suppressed by the square of the Planck length in units of the horizon radius, $\ell_{\rm pl}^{2}/r_{\rm h}^{2}$. This is consistent with the classical vanishing being a consequence of an accidental symmetry of static general relativity, broken by quantum loops. Extrapolated to gravitational perturbations, our results suggest that the quadrupolar static Love numbers of Schwarzschild are of size $λ\sim M r_{\rm h}^{2} \ell_{\rm pl}^{2}$.
Comments22 pages + appendices
