| Abstract: | The internal structure of black holes has crucial implications on the fate of infalling probes or observers. We numerically investigate the interior of charged black holes with scalar-field perturbation. Previous study suggested that late infalling observers would encounter an effective shock wave at the inner horizon; the shock manifests as an effective jump in the values of the perturbation field and the metric itself. We confirm this prediction numerically by demonstrating the sharp proper-time evolution of the scalar and metric fields along timelike geodesics. We also confirm the prediction about shock sharpening rate; in addition we probe the early stages of shock formation. To this end we developed a finite-differences numerical code with double-null coordinates and an adaptive gauge method. This allows us to simulate spacetime evolution from the weak-field region outside the black hole up to the vicinity of the Cauchy horizon and the r=0 singularity.
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