Observability and Identifiability of Quantum Near-Extremal Black Holes

Quantum fluctuations of a near-AdS2 throat can strongly modify low-frequency scattering while spacetime curvature remains small. A large quantum correction, however, need not be observable in finite time, and an observable correction need not identify the state that produced it. We formulate these distinctions for an initially spinless, near-extremal Reissner-Nordström black hole. First, we impose three operational gates: finite-time spectral resolution, nondisruptive probing, and statistical/systematic distinguishability. Passive emission is disfavored by entropy suppression and low event rates, whereas active scalar absorption can possess a principle-level window in which the probe is classical, the throat remains quantum, and the enhanced cross-section is distinguishable. Second, we formulate the inverse problem. In the zero-frequency limit, the scalar response depends only on x = E_i/E_b and therefore cannot separately identify the excitation energy E_i and the Schwarzian scale E_b. Finite-frequency spectral information can lift this scaling degeneracy. More sharply, fixed-helicity photon and graviton transparency thresholds satisfy ω_γ = E_b − E_i and ω_g = 3E_b − E_i, yielding the exact inversion E_b = (ω_g − ω_γ)/2 and E_i = (ω_g − 3ω_γ)/2. The two-threshold Jacobian has determinant −2 and condition number approximately 5.83. Threshold-inferred parameters also predict the scalar response, providing a cross-channel null test of the Schwarzian description. Our claims are structural and principle-level; they do not constitute an astrophysical detector forecast.