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Probing a polymerized black hole with the frequency shifts of photons
As is well-known, black hole plays an important role in probing the quantum
effects of gravity in the strong-field regime. In this paper, we focus on a
polymerized black hole and investigate the quantum effects on the redshift,
blueshift and gravitational redshift of photons emitted by massive particles
revolving around this black hole. With a general relativistic formalism, we
obtain two elegant and concise expressions for the mass of the black hole and
the quantum parameter in terms of few direct observables, and find that all the
frequency shifts of photons decrease with the quantum parameter. By expanding
the total frequency shift for large orbit of the emitter, low peculiar
redshift, and small azimuthal angle, we find that the leading contributions to
the frequency shift are originated from the kinematic shift and peculiar shift,
and the quantum effects make a negligible contribution. In addition, we study
the effects of the plasma on the redshift/blueshift for the first time, and
conclude that the presence of plasma results in the decrease of the
redshift/blueshift.Comment: 8 pages, 2 figures; published in Physical Review
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