Logarithmic Corrections for Near-extremal Kerr-Newman Black Holes

TL;DR

This paper calculates logarithmic entropy corrections for near-extremal Kerr-Newman black holes in supergravity, addressing zero mode divergences and providing results that any microscopic theory should reproduce.

Contribution

It introduces a novel modified heat kernel approach to compute near-extremal corrections for charged rotating black holes in supergravity.

Findings

Logarithmic entropy corrections computed for near-extremal Kerr-Newman black holes.

Addressed zero mode divergences in the Euclidean path integral approach.

Provided a method for matching microscopic entropy calculations.

Abstract

In this paper, we have computed the logarithmic corrections of entropy for the near-extremal Kerr-Newman black holes in $\mathcal{N}=2$ supergravity theory applying the Euclidean path integral approach in the near-horizon geometry. In the near-horizon extremal Kerr geometry, analogous to the $AdS_{2} \times S^2 $ structure, there exists a set of normalizable zero modes associated with reparametrizations of boundary time. The one-loop approximation to the Euclidean near-horizon extremal Kerr partition function exhibits an infrared divergence due to the path integral over these zero modes. Carrying out the leading finite temperature correction in the near-horizon extremal Kerr scaling limit, we control this divergence. Considering the near-extremal near-horizon geometry as a perturbation around the extremal near-horizon geometry, we determine these corrections implementing a modified heat kernel approach which involves both the extremal and near-extremal corrections and is novel in the literature for the charged rotating black holes in supergravity theory. This result should be reproduced by any microscopic theory that explains the entropy of the black hole.