Logarithmic corrections to the entropy for near-extremal rotating black holes

An interesting feature of quantum corrections to the Bekenstein--Hawking entropy is the appearance of logarithmic area terms, whose coefficients are governed by the spectrum of massless fields. For near-extremal black holes, the entropy also receives a logarithmic temperature corrections, whose coefficient is determined by the zero modes of the corresponding extremal black holes. In this paper, we study near-extremal rotating black holes in three, four, and five dimensions with an important focus on rotational zero modes. For three-dimensional BTZ black holes, our results are in agreement with the microscopic description. Furthermore, by treating the cosmological constant scale \(\ell\) as an independent parameter, we find an additional \(\log \ell\) correction to the entropy at extremality. For the five-dimensional BMPV black hole, we explicitly construct all the extremal zero modes and use them to evaluate the log temperature corrections to the entropy.