Abstract

We construct an exactly solvable effective exterior quantum source coupled to the massless scalar field on Schwarzschild. The benchmark is restricted to the s-wave sector and uses a spatially extended source with full angular-shell support. A degenerate qubit controls a smooth compact linear field interaction in normalized Killing time. We construct its unitary propagator, including the finite time-ordering phase, in a regular representation of the inherited Unruh state.

Tracing the source gives a measure-and-prepare field channel. Its restriction to finitely many identified outgoing scalar packets is a normal channel whose two conditional outputs are oppositely displaced versions of the semiclassical Gaussian baseline. All source matrix units are evaluated. The channel transmits a classical source observable but is entanglement breaking. For a finite packet output, its optimal deterministic recovery error is expressed through the trace distance of the two conditional radiation states and is strictly greater than one half at every finite coupling.

We prove a nonzero outgoing signal for a compact separable exterior profile. A bounded sine-Weyl effect distinguishes the source signs, whereas all selected joint number probabilities are identical for those signs. The phase-sensitive gap is linear at weak coupling, while the occupation-mean departure is quadratic.

A compact local scalar probe realizes the sine-effect comparison. We verify a common second-moment bound for the source-displaced states and give separate packet, transfer, probe-noise, profile, readout, and statistical allowances. The local construction uses growing full-shell access, a scaled processing test, and a specified squeezed probe preparation. Causal support, retained-source dephasing, finite excess radiative energy, and switching work are calculated separately.

The source law is a declared exterior model, not a derivation from microscopic quantum gravity. No information escape from a black-hole interior, coherent local field transfer, or evaporation theorem is established.