Researchers have calculated the one-loop quantum corrections to the entropy of near-extremal black holes within the framework of three-dimensional New Massive Gravity (NMG). This work focuses on a specific point in NMG theory where a unique maximally symmetric vacuum exists and where "hairy" black holes with non-constant curvature can achieve extremality even in a static state. The study addresses the near-horizon AdS$_2\times S^1$ geometry of these black holes.

The methodology involved evaluating the contribution of boundary graviton modes, which become exact zero modes in the extremal limit. By analyzing the resulting one-loop partition function, the scientists demonstrated that it generates logarithmic corrections to the semiclassical entropy. This finding represents a significant extension to higher-curvature gravity theories of results previously obtained for near-extremal black holes in General Relativity.

This advance is relevant because black hole entropy, a key concept in black hole thermodynamics, is an active area of research in the quest for a quantum theory of gravity. Logarithmic corrections are often indicative of low-energy quantum effects and can offer clues about the microstructure of black holes. The ability to apply these calculations to higher-curvature gravity theories like NMG expands the scope of our understanding beyond standard General Relativity.