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The rather elusive High-Frequency Quasi-Periodic Oscillations(HFQPO) observedin the X-ray lightcurve of black holes have been seen in a wide range offrequencies, even within one source. It is also notable to have been detectedin "pairs" of HFQPOs with a close to integer ratio between the frequencies. Theaim of this paper is to investigate some of the possible observable that wecould obtain from having the Rossby Wave Instability (RWI) active in theaccretion disc surrounding the compact object.  Using the newly developed GR-AMRVAC code able to follow the evolution of theRWI in a full general relativistic framework, we explore how RWI can reproduceobserved HFQPO frequencies ratios and if it is compatible with theobservations. In order to model the emission coming from the disc we havelinked our general relativistic simulations to the general relativisticray-tracing GYOTO code and delivered synthetic observables that can beconfronted to actual data from binary systems hosting HFQPOs.}{We havedemonstrated in our study that some changes in the physical conditionsprevailing in the part of the disc where RWI can be triggered leads to variousdominant RWI modes whose ratio recovers frequency ratios observed in variousX-ray binary systems. In addition, we have also highlighted that when RWI istriggered near the last stable orbit of a spinning black hole, the amplitude ofthe X-ray modulation increases with the spin of the black hole. Revisitingpublished data on X-ray binary systems, we show that this type of relationshipactually exists in the five systems where an indirect measure of the spin ofthe black hole is available.

Rossby Wave Instability and High-Frequency Quasi-Periodic Oscillations in accretion discs orbiting around black holes