where the integration is done on the (n − 1)-dimensional spacelike hypersurface of Killing horizon, ˜g μν is the induced metric on it, ˜g
is the determinant of ˜gμν and ˜L k is the kth order Lovelock Lagrangian of ˜g μν. The asymptotic behavior of the black branes we are
considering is not flat, and therefore we calculate the entropy through the use of Gibbs–Duhem relation