Logarithmic corrections for near-extremal black holes

We present the computation of logarithmic corrections to near-extremal black hole entropy from one-loop Euclidean gravity path integral around the near-horizon geometry. We extract these corrections employing a suitably modified heat kernel method, where the near-extremal near-horizon geometry is treated as a perturbation around the extremal near-horizon geometry. Using this method we compute the logarithmic corrections to non-rotating solutions in four dimensional Einstein-Maxwell and $\mathcal{N}$ \( \mathcal{N} \) = 2, 4, 8 supergravity theories. We also discuss the limit that suitably recovers the extremal black hole results.