Viscosity to entropy density ratio for non-extremal Gauss–Bonnet black holes coupled to Born–Infeld electrodynamics

Abstract

Abstract The ratio of the shear viscosity to the entropy density ( $$\eta /s$$ η / s ) is calculated for non-extremal black holes in D dimensions with arbitrary forms of the matter Lagrangian for which the space-time metric takes a particular form. The result reduces to the standard expressions in 5 dimensions. The $$\eta /s$$ η / s ratio is then computed for Gauss–Bonnet black holes coupled to Born–Infeld electrodynamics in 5 dimensions. As a result we found corrections as regards the BI parameter and th result is analytically exact up to all orders in this parameter. The computations are then extended to D dimensions.