Stationary scalar clouds, quasinormal ringing, and observational signatures of (near-)extremal rotating Kalb-Ramond black holes: from the superradiant threshold to EHT bounds

Abstract

We study a massive scalar field on the rotating Kalb-Ramond black hole of Kumar, Ghosh and Wang, in the (near-)extremal corner of its three-parameter family $(a,\gamma,\lambda)$. We verify by direct substitution that the Klein-Gordon-Fock equation separates on this background, with radial and angular separation constants related by $\Lambda_{rad}=\Lambda_{ang}+a^2\omega^2-2am\omega$. At exact extremality the horizon polynomial and the function $K(r)$ share a zero, rendering $K^2/\Delta$ regular there and reducing the radial problem to Whittaker form on the Kerr line $(\gamma=0)$ and the Kerr-Newman line $(\lambda=1)$. The stationary resonances saturate $\omega=m\Omega_H$ and satisfy the bound-state condition $\mu>m\Omega_H$, with overtones accumulating at the threshold from above; in the genuinely Kalb-Ramond interior we solve the exact radial equation as a two-point boundary value problem. Moving off extremality, the clouds continue onto the co-rotating zero-damped branch $\omega_n=m\Omega_H-i\kappa(n+1/2+\beta)$, governed by the same near-horizon exponent $\beta$; the photon-sphere family is a distinct observable. Greybody factors and superradiant amplification are obtained by direct integration, recovering the classical scalar amplification on Kerr. Strong-field lensing is treated in the Bozza-Tsukamoto limit with rotating photon orbits of both senses, where the prograde logarithmic coefficient departs strongly from its Schwarzschild value. The shadow contour follows from the Carter-Hamilton-Jacobi separation. Crossing the Event Horizon Telescope window of Zubair, Raza and Maqsood with the cloud-existence region yields a narrower bound on the Lorentz-violating parameters $(\gamma,\lambda)$ than either constraint alone.