Constraints on the rotating self-dual black hole with quasi-periodic oscillations

An impressive feature of loop quantum gravity (LQG) is that it can elegantly resolve both the big bang and black hole singularities. By using the Newman -Janis algorithm, a regular and effective rotating self -dual black hole (SDBH) metric could be constructed, which alters the Kerr geometry with a polymeric function P from the quantum effects of LQG geometry. In this paper, we investigate its impact on the frequency characteristics of the X-ray quasi -periodic oscillations (QPOs) from 5 X-ray binaries and contrast it with the existing results of the orbital, periastron precession and nodal precession frequencies within the relativistic precession model. We apply a Monte Carlo Markov Chain (MCMC) simulation to examine the possible LQG effects on the X-ray QPOs. We found that the best constraint result for the rotating self -dual geometry from LQG came from the QPOs of X-ray binary GRO J1655-40, which establish an upper bound on the polymeric function P less than 6.15 x 10-3 at 95% confidence level. This bound leads to a restriction on the polymeric parameter delta of LQG to be 0.66.