Universality in the relaxation dynamics of the composed black-hole-charged-massive-scalar-field system: The role of quantum Schwinger discharge

The quasinormal resonance spectrum {ωn(μ,q,M,Q)}n=0n=∞ of charged massive scalar fields in the charged Reissner–Nordström black-hole spacetime is studied analytically   in the large-coupling regime qQ≫MμqQ≫Mμ (here {μ,q}{μ,q} are respectively the mass and charge coupling constant of the field, and {M,Q}{M,Q} are respectively the mass and electric charge of the black hole). This physical system provides a striking illustration for the validity of the universal relaxation bound τ×T≥ħ/πτ×T≥ħ/π in black-hole physics (here τ≡1/ℑω0τ≡1/ℑω0 is the characteristic relaxation time of the composed black-hole-scalar-field system, and T is the Bekenstein–Hawking temperature of the black hole). In particular, it is shown that the relaxation dynamics of charged massive scalar fields in the charged Reissner–Nordström black-hole spacetime may saturate this quantum time-times-temperature inequality. Interestingly, we prove that potential violations of the bound by light scalar fields are excluded by the Schwinger-type pair-production mechanism (a vacuum polarization effect), a quantum   phenomenon which restricts the physical parameters of the composed black-hole-charged-field system to the regime qQ≪M2μ2/ħqQ≪M2μ2/ħ.