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Modified Dispersion Relations and Black Hole Entropy

We compute the black hole entropy in the context of the Modified Dispersion Relations using the brick wall model. An explicit dependence of the radial coordinate approaching the horizon is shown to analyze the behavior of the divergence. We find that, due to the modification of the density of states, the brick wall can be eliminated. By assuming a specific form for the radial coordinate $r(E/E_{P}) $, we examine a possible candidate for $r(E/E_{P}) $. A comparison with the 't Hooft approach is presented.