• Newman-Janis algorithm
• quantum-improved black holes
• quantum gravity
• quantum improvement
• asymptotically safe gravity
• asymptotic safety
• quantum-improved black holes thermodynamics

The search for a consistent theory of quantum gravity has been a central challenge in theoretical physics for decades. While general relativity successfully describes the classical behaviour of gravity, it encounters several difficulties when treated as a quantum theory. The quest to unify the principles of the Standard Model with those of general relativity has prompted the exploration of alternative approaches, including the concept of Asymptotically Safe Gravity (ASG). 

This thesis aims to explore the implications of ASG-based quantum improvement on both the Schwarzschild and Kerr black holes. To achieve this, we use the "running" scale-dependent Newton’s coupling of the theory, proposed by Bonanno and Reuter. More specifically, to implement the concept of quantum improvement, we replace Newton’s constant of gravity with the running coupling in the Schwarzschild metric, resulting in the quantum-improved Schwarzschild metric. Additionally, we extend the investigation to the quantum-improved Kerr metric using a modified version of the Newman-Janis algorithm, which generates rotating, axially symmetric metrics from static, spherically symmetric metrics.

We specifically focus on how the quantum improvement changes the structure of the spacetimes under examination and its implications within the framework of thermodynamics. The research work raises questions regarding the computation of entropy for quantum-improved black holes, which we leave open for future research endeavours.