We study the emission of gravitational waves by EMRIs in numerically produced spacetimes which are highly accurate solutions of Einstein equations and contain a black hole and a torus. In order to assess the maximal impact these tori could have on the produced waveforms, we consider them as compact, massive and close to the central black hole and try to determine whether LISA can detect their presence. Our results reinforce the confusion problem recently pointed out in [1].

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