Abstract

We construct a compactly coupled scalar probe scheme for one bounded outgoing Hawking-packet quadrature effect on the Schwarzschild exterior. The result is restricted to a massless s-wave packet and uses full angular-shell access.

Complete stationary scattering identifies the packet with a two-channel bulk coefficient. We construct real, compactly supported bulk tests approaching that coefficient in the Unruh covariance norm. A time-derivative filter permits a quantitative spatial Cauchy-data truncation without assuming that the thermal low-frequency weight is harmless. Separately, the explicit zero-energy s-wave solutions give a local infrared bound for arbitrary compact reduced tests.

A second massless scalar is coupled to the system by a smooth compact bilinear interaction. We calculate the exact induced Weyl effect and bound its deviation from the selected compact bulk test by a convergent advanced-Green-operator construction. Residual probe noise is retained. A finite-dimensional symplectic squeezing of the probe preparation suppresses that noise while keeping the probe readout a bounded effect; dividing an effect by its attenuation coefficient is not used.

The resulting expectation comparison is uniform on an explicitly defined class of regular system states with dominated second moments. It specializes to the inherited Unruh baseline and has a constructive resource-dependent accuracy schedule. The coupling region expands with the packet approximation, the readout test grows at weak coupling, and a conjugate probe variance diverges along the noise-suppression schedule.

This is a local field–probe observable correspondence, not a pointlike detector, a packet-number instrument, coherent state transfer, or channel equivalence with the effective apparatus of Em03-C. No collapse geometry, microscopic evaporation dynamics, or quantum-gravity correction is constructed.