Stationary scalar clouds, quasinormal ringing, and observational signatures of (near-)extremal rotating Kalb-Ramond black holes: from the superradiant threshold to EHT bounds
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 $(a,γ,λ)$. We verify by direct substitution that the Klein-Gordon-Fock equation separates on this background, with radial and angular separation constants related by $Λ_{rad}=Λ_{ang}+a^2ω^2-2amω$. At exact extremality the horizon polynomial and the function $K(r)$ share a zero, rendering $K^2/Δ$ regular there and reducing the radial problem to Whittaker form on the Kerr line $(γ=0)$ and the Kerr-Newman line $(λ=1)$. The stationary resonances saturate $ω=mΩ_H$ and satisfy the bound-state condition $μ>mΩ_H$, 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 $ω_n=mΩ_H-iκ(n+1/2+β)$, governed by the same near-horizon exponent $β$; 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 $(γ,λ)$ than either constraint alone.