We investigate the stress tensor for holographic fluids at the finite cutoff surface through perturbing the Schwarzchild-AdS black brane background to the first order perturbations in the scenario of fluid/gravity correspondence. We investigate the most general perturbations of the metric without any gauge fixing. We consider various boundary conditions and demonstrate the properties of the corresponding holographic fluids. The critical fact is that the spatial components of the first order stress tensors of the holographic fluids can be rewritten in a concordant form, which implicates that there is an underlying universality in the first order stress tensor. We find this universality in the first order stress tensor for holographic fluids at the finite cutoff surface by an exhaustive investigation of perturbations of the full bulk metric.
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