极端非旋转黑洞无费米型洛夫数
Extremal non-rotating black holes have no fermionic Love
AI总结：
本文通过推导任意渐近平直黑洞静态费米型TLN的闭式公式，证明极端静态球对称黑洞的费米型TLN为零，分析了两类黑洞的极端构型的TLN特性。
AI中文摘要：
四维黑洞的静态潮汐洛夫数（TLN）对于玻色型微扰为零，但对于费米型微扰通常非零，仅存在少数例外。本文中，我们证明对于静态、球对称黑洞，费米型TLN为零当且仅当该黑洞是极端黑洞，即其视界是简并的。这一结论源于任意渐近平直黑洞的静态费米型TLN的闭式公式，该公式通过在任意此类时空上精确求解静态无质量狄拉克方程并要求视界处正则性得到。作为应用，我们分析了Simpson–Visser正则黑洞和圈量子引力残余黑洞，它们的极端构型导致费米型TLN为零而玻色型TLN非零。
英文摘要：
The static tidal Love numbers (TLNs) of $4$-dimensional black holes vanish for bosonic perturbations but are generically nonzero for fermions, with rare exceptions. In this paper, we show that for static, spherically symmetric black holes, fermionic TLNs vanish if and only if the black hole is extremal, in the sense that its horizon is degenerate. This follows from a closed formula for the static fermionic TLN of any asymptotically flat black hole, obtained by solving the static massless Dirac equation exactly on an arbitrary such spacetime and imposing regularity at the horizon. As applications, we analyze the Culetu--Simpson--Visser regular black hole and the loop-quantum-gravity remnant black holes, whose extremal configurations lead to vanishing fermionic yet nonvanishing bosonic TLNs.
