Logarithmic corrections for near-extremal Kerr-Newman Black holes

A bstract In this paper, we computed the logarithmic corrections of entropy for the near-extremal Kerr-Newman black holes in $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 supergravity theory applying the Euclidean path integral approach in near-horizon geometry. In the near-horizon extremal Kerr geometry, analogous to the AdS 2 × S 2 structure, there exists a set of normalizable zero modes associated with reparameterization of boundary time. The one-loop approximation to the Euclidean near-horizon extremal Kerr partition function exhibits an infrared divergence because of 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. Further, treating the near-horizon geometry of the near-extremal black hole as a perturbation around its extremal counterpart, we computed the corresponding corrections using a modified heat kernel approach. This method incorporates both extremal and near-extremal contributions and represents a novel solution within the context of charged rotating black holes in $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 2 supergravity theories.