Editing Openai/6897769e-4ee4-800f-aba5-69cca34f701c (section)

===== 1. Model: Bulk action (AdS4_44) with metric gMNg_{MN}gMN, U(1) gauge field AMA_MAM, and minimal Einstein–Maxwell action. Boundary is S2^22×time (your spherical shells). =====
# Boundary data: Turn on a time-dependent boundary source Aa(0)(t,Ω)A^{(0)}_a(t,\Omega)Aa(0)(t,Ω) modelling the QAT photon field hitting the shell and a boundary current Ja(t,Ω)J^a(t,\Omega)Ja(t,Ω) with dissipative spectral density.
# Compute: Use linear response / GKPW to compute the bulk field solution and the backreaction on the bulk metric to leading order (compute metric perturbation hMNh_{MN}hMN from boundary stress TabT_{ab}Tab built from the current correlator).
# Question answered: Does a plausible boundary spectral density produce a bulk metric perturbation with Newtonian 1/r behaviour in the near-boundary limit? How does the induced bulk stress scale with boundary parameters?

This is the minimum to see whether boundary dissipative processes can seed metric perturbations of the right qualitative form.