Thermal fluctuation effects on shear viscosity to entropy ratio in five-dimensional Kerr–Newman black holes

Abstract We investigate how thermal fluctuations affect the properties of five-dimensional Kerr–Newman black holes, focusing particularly on the shear viscosity to entropy ratio. Our analysis incorporates logarithmic corrections to the Bekenstein–Hawking entropy and examines their impact on black hole thermodynamics. We explore three approaches to studying the shear viscosity-entropy ratio in the presence of thermal fluctuations: considering independent shear viscosity, thermally corrected shear viscosity, and an independent ratio assumption. Notably, we find that the lower bound of $$\eta /S \ge 1/4\pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>η</mml:mi> <mml:mo>/</mml:mo> <mml:mi>S</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>4</mml:mn> <mml:mi>π</mml:mi> </mml:mrow> </mml:math> remains valid even with thermal fluctuations, though the specific behavior depends on the black hole mass and correction parameter. Our results suggest that thermal fluctuations generally decrease the ratio for massive black holes while maintaining the universal lower bound. This work extends our understanding of quantum corrections to black hole transport properties.