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The recent announcement of the detection of gravitational waves by theLIGO/Virgo collaboration has opened a new window to test the nature ofastrophysical black holes. Konoplya & Zhidenko have shown how the LIGO data ofGW 150914 can constrain possible deviations from the Kerr metric. In thisletter, we compare their constraints with those that can be obtained fromaccreting black holes by fitting their reflected X-ray spectrum, the so-callediron line method. We simulate observations with eXTP, a next generation X-raymission, finding constraints much stronger than those obtained by Konoplya &Zhidenko. Our results can at least show that, contrary to what is quitecommonly believed, it is not obvious that gravitational waves are the mostpowerful approach to test strong gravity. In the presence of high quality dataand with the systematics under control, the iron line method may providecompetitive constraints.

Testing the Kerr black hole hypothesis: comparison between the gravitational wave and the iron line approaches