在廣義相對論中，黑洞解通常包含奇點，這標誌著古典理論的失效。為了解決此問題，漸進安全計畫（asymptotic safety program）被用來藉由將紐頓常數與宇宙常數推廣為隨尺度變化的跑動耦合常數（running couplings），進而在解的層面納入量子效應。雖然透過跑動耦合常數來修飾時空提供了一個消除奇點的潛在機制，但相關的黑洞熱力學機制卻經常被忽略。在本論文中，我們證明了黑洞熱力學第一定律的自洽性，為可接受的尺度識別（scale identifications）提供了根本的約束。對於不依賴質量的系統，我們發現熱力學自洽性要求跑動耦合常數必須僅依賴於事件視界的面積。為了進一步消除旋轉黑洞的環狀奇點，我們延伸了此一原理，並推導出一種新型的「質量依賴型」跑動耦合常數。由此得到的量子修正解不僅成功消除了奇點，同時也抑制了封閉時間類曲線（closed timelike curves）的形成。;In General Relativity， black hole solutions generically contain singularities， signaling the breakdown of the classical theory. To address this issue， the asymptotic safety program has been employed to incorporate quantum effects at the level of the solution by promoting the Newton and cosmological constants to scale-dependent running couplings. Although modifying spacetime through running couplings offers a promising mechanism for resolving singularities， the associated black hole thermodynamics are often neglected. In this thesis， we demonstrate that the consistency of the first law of black hole thermodynamics provides a fundamental constraint on admissible scale identifications. For the mass-independent case， we find that thermodynamic consistency requires the running coupling to depend solely on the horizon area. To resolve the ring singularity of rotating black holes， we further extend this principle and derive a novel mass-dependent running coupling. The resulting quantum-improved solution successfully removes the singularity and suppresses the formation of closed timelike curves.
