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We analyze numerically the violation of the fluctuation-dissipation theorem(FDT) in the $\pm J$ Edwards-Anderson (EA) spin glass model. Using single spinprobability densities we reveal the presence of strong dynamicalheterogeneities, which correlate with ground state information. The physicalinterpretation of the results shows that the spins in the EA model can bedivided in two sets. In 3D, one set forms a compact structure which presents acoarsening-like behavior with its characteristic violation of the FDT, whilethe other asymptotically follows the FDT. Finally, we compare the dynamicalbehavior observed in 3D with 2D.Comment: Accepted for publication in Phys. Rev. Lett. 200

Strong Dynamical Heterogeneities in the Violation of the Fluctuation-Dissipation Theorem in Spin Glasses