Quasinormal Modes, Partial Transmission Probabilities, and Hod's Conjecture of Charged Black Holes in Perfect Fluid Dark Matter within Kalb-Ramond Gravity

Abstract

Within the Kalb-Ramond field-induced Lorentz-violating gravity, we investigate the perturbation dynamics and quasinormal mode (QNM) spectra of a charged black hole immersed in perfect fluid dark matter. The background spacetime is characterized by the Lorentz-violating parameter tau, the electric charge Q/M, and the dark matter parameter lambda/M. Owing to the non-zero vacuum expectation value of the KR field, the metric function approaches 1/(1-tau) at infinity instead of 1, rendering the spacetime non-asymptotically flat. Under the test-field approximation, the equations of motion for three types of perturbations (scalar, electromagnetic, and axial gravitational) are reduced to Schrodinger-type radial equations with single-peak effective potentials. The QNM frequencies are cross-validated using the sixth-order WKB method and the time-domain Prony method, while the partial transmission probabilities are computed within the WKB scattering framework. Parameter scans show that tau exerts the strongest influence on the QNM spectrum, followed by lambda/M, with Q/M having the weakest effect; the same ordering holds for the partial transmission probabilities. Under the same parameters, the QNM frequencies of the three perturbations follow the order scalar > electromagnetic > gravitational, whereas the transmission probabilities exhibit the reverse order, reflecting the different impact of the effective potential height on the oscillation frequency and on the transmission probability. The Hod conjecture |Im(omega)| <= pi T_H holds throughout the parameter range examined.