Kalb-Ramond引力中处于理想流体暗物质里的带电黑洞的准正态模式、部分透射概率与Hod猜想
Quasinormal Modes, Partial Transmission Probabilities, and Hod's Conjecture of Charged Black Holes in Perfect Fluid Dark Matter within Kalb-Ramond Gravity
AI总结：
本文在Kalb-Ramond引力框架下，研究理想流体暗物质中带电黑洞的扰动与QNM谱，发现Hod猜想成立，明确了各参数对QNM谱及透射概率的影响规律。
AI中文摘要：
在Kalb-Ramond（KR）场诱导的洛伦兹破缺引力框架下，我们研究了浸没在理想流体暗物质中的带电黑洞的扰动动力学与准正态模式（QNM）谱。该背景时空由洛伦兹破缺参数τ、电荷与质量比Q/M以及暗物质参数λ/M表征。由于KR场的非零真空期望值，度规函数在无穷远处趋近于1/(1−τ)而非1，致使该时空非渐近平直。在测试场近似下，三类扰动（标量、电磁、轴向引力）的运动方程被约化为具有单峰有效势的薛定谔型径向方程。采用六阶WKB方法与时域Prony方法对QNM频率进行交叉验证，同时在WKB散射框架内计算了部分透射概率。参数扫描显示，τ对QNM谱的影响最强，其次是λ/M，Q/M的影响最弱；部分透射概率也遵循相同的排序。在相同参数下，三类扰动的QNM频率遵循标量>电磁>引力的顺序，而透射概率则呈现相反顺序，反映了有效势高度对振荡频率与透射概率的不同影响。在所考察的全部参数范围内，Hod猜想|Im(ω)|≤πT_H成立。
英文摘要：
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.
