Quantum Improved Kerr Black Holes and Thermodynamics
ABSTRACT
The asymptotic safety approach to the quantum gravity suggests that the Newton coupling depends on the energy scale. To make connection to the black hole geometry, we have to identify the energy scale to certain length scale, but there has not been any principle to constrain the identification. We show that the first law of the thermodynamics gives quite nontrivial constraint on the identification, and this leads to interesting consequences on the expression of the entropy and black hole geometry. The quantum improved entropy reduces to the Bekenstein-Hawking formula in the semi-classical limit, and suitable choice of the identification leads to the possibility of singularity resolution.