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An outstanding prediction of general relativity is the fact that the angularmomentum $S$ of an isolated black hole with mass $\mu$ is limited by the Kerrbound, $S\leq G\mu^2/c$. Testing this cornerstone is challenging due to thedifficulty in modelling spinning compact objects that violate this bound. Weargue that precise, model-independent tests can be achieved by measuringgravitational waves from an extreme mass ratio inspiral around a supermassiveobject, one of the main targets of the future LISA mission. In the extreme massratio limit, the dynamics of the small compact object depends only on itsmultipole moments, which are free parameters. At variance with thecomparable-mass case, accurate waveforms are valid also when the spin of thesmall object greatly exceeds the Kerr bound. By computing the orbital dephasingand the gravitational-wave signal emitted by a spinning point particle incircular, nonprecessing, equatorial motion around a Kerr black hole, weestimate that LISA will be able to measure the spin of the small compact objectat the level of $10\%$. Together with mass measurements, this will allow fortheory-agnostic, unprecedented constraints on string-theory inspired objectssuch as "superspinars", almost in their entire parameter space.

Model independent tests of the Kerr bound with extreme mass ratio inspirals