One-loop Corrected Thermodynamics of the Extremal and Non-extremal Spinning Btz Black Hole

We consider the one-loop corrected geometry and thermodynamics of a rotating BTZ black hole by way of a dimensionally reduced dilaton model. The analysis begins with a comprehensive study of the non-extremal solution after which two different methods are invoked to study the extremal case. The first approach considers the extremal limit of the non-extremal calculations, whereas the second treatment is based on the following conjecture: extremal and non-extremal black holes are qualitatively distinct entities. We show that only the latter method yields regularity and consistency at the one-loop level. This is suggestive of a generalized third law of thermodynamics that 1 forbids continuous evolution from non-extremal to extremal black hole ge-ometries.