Constraining Lorentz Violation in Kalb-Ramond Gravity via Thermodynamics and Gravitational Wave Analysis

We constrain spontaneous Lorentz symmetry breaking by analyzing the observational signatures of a static black hole in a Kalb-Ramond (KR) background. We demonstrate that thermodynamic consistency requires time coordinate renormalization to the physical frame. Modeling the ringdown phase via a third-order WKB approximation, we find that the Lorentz-violating parameter $l$ induces distinct "spectral hardening" of quasinormal modes and suppresses the optical shadow radius as $R_{sh} \propto \sqrt{1-l}$.  Although a geometric degeneracy exists between the KR model and a scaled-mass Schwarzschild black hole, we break this degeneracy by incorporating independent mass priors for Sagittarius A* from S2 stellar dynamics. Comparing theoretical predictions with Event Horizon Telescope (EHT) imaging, we establish a robust upper bound of $l \lesssim 0.19$ at the $1\sigma$ confidence level.