  Recently the Petrov type I condition is introduced to reduce the degrees of
freedom in the extrinsic curvature of a timelike hypersurface to the degrees of
freedom in the dual Rindler fluid in Einstein gravity. In this paper we show
that the Petrov type I condition holds for the solutions of vacuum
Einstein-Gauss-Bonnet gravity up to the second order in the relativistic
hydrodynamic expansion. On the other hand, if imposing the Petrov type I
condition and Hamiltonian constraint on a finite cutoff hypersurface, the
stress tensor of the relativistic Rindler fluid in vacuum Einstein-Gauss-Bonnet
gravity can be recovered with correct first order and second order transport
coefficients.
