Testing gravity of a regular and slowly rotating phantom black hole by quasi-periodic oscillations

We extend firstly the regular phantom black hole solution to a slowly rotating black hole case and find that the phantom field depresses the angular velocity of the event horizon and suppresses the super-radiation of black hole. We also probe the dependence of quasi-periodic oscillations frequencies in relativistic precession model on the phantom parameter. With the observation data of GRO J1655-40, we make a constraint on the parameters of the regular and slowly rotating phantom black hole. Our results show that although the best-fit value of the phantom parameter $b$ is small, the allowed value of $b$ in the $1\sigma$ region is $b<0.619$, which means that the phantom theoretical model can not be excluded by the constraint from quasi-periodic oscillations with the observation data of GRO J1655-40.