A new way to calculate black hole mass using alternative gravity?

Teleparallel gravity rewrites Einstein's theory using tetrads instead of curvature, but lacks a clean field-theory toolkit. This work builds one from scratch — a Lagrangian framework where gravitational perturbations propagate on any background, with proper gauge invariance and conserved charges via Noether's theorem. As a sanity check, it recovers the correct mass and angular momentum for Schwarzschild and Kerr black holes, and derives standard gravitational wave equations in TT-gauge.