An Effective Relational Field Theory for Gravitational Stasis: Vainshtein Screening, Strong-Field Galileon Dynamics, and Dissipative Boundary Phenomenology

We investigate a four-dimensional effective field theory (EFT) motivated by relational quantum state transitions and local informational saturation bounds. Spacetime geometry is treated as an emergent macroscopic description arising from an Einstein-Hilbert sector coupled to a shift-symmetric cubic Galileon order parameter, , whose kinetic gradients parameterize the local processing rate of quantum state updates. Standard Model matter couples universally to an emergent disformal metric governed by an energy scale . Working in natural units () with the reduced Planck mass , the scalar field carries canonical mass dimension , and the cubic Galileon coupling is fixed by a dimensionless parameter . In the weak-field regime, non-linear Vainshtein screening suppresses scalar fifth forces by a factor of , maintaining compatibility with precision solar-system tests (Cassini parameter ) without fine-tuning standard gravity. In the strong-field limit, we carry out an exact, non-approximated functional variation of the cubic action to determine the scalar energy-momentum tensor . We demonstrate that under the vanishing radial Noether current condition (), all terms containing cancel identically in the radial component, reducing the radial stress-energy strictly to . Confronting this with the stationary Einstein constraint at a candidate turning point ( with ), the canonical branch () is analytically excluded due to a strict sign contradiction ( while ). Conversely, the non-trivial Galileon branch () generates a negative kinetic radial pressure, satisfying the necessary algebraic condition and lifting the leading-order sign obstruction. To examine whether this local turning point admits a regular, horizonless metric minimum (), we perform a Frobenius Taylor expansion around and implement an adaptive two-point boundary-value shooting algorithm. We demonstrate analytically that the radial equation alone cannot fix the sign of without the simultaneous solution of and . Numerically, the shooting scan reveals that the pure cubic Galileon sector fails to sustain a regular minimum connected smoothly to an asymptotic Schwarzschild vacuum (), establishing a dynamic no-go theorem for pure cubic Horndeski stasis and demonstrating the mandatory requirement of higher-order interactions (). Consequently, the subsequent analysis of horizon absorption, thermodynamics, and gravitational-wave signatures is formulated as an effective phenomenological framework for horizonless Exotic Compact Objects (ECOs). Analyzing open strain data from the LIGO/Virgo GWOSC repository across four binary black hole mergers (GWTC-1), a coherent stacked search yields an effective global significance of (accounting for independent trials), fully consistent with instrumental noise and ruling out macroscopic elastic reflections (). This motivates modeling the boundary as an effective dissipative absorber adhering to the Kovtun-Son-Starinets (KSS) viscosity bound (). Semiclassical evaporation is regularized via a Planck-mass saturation ansatz, terminating at an inert remnant () with finite area and bounded entropy . Finally, in extreme-mass-ratio inspirals (EMRIs), boundary dissipation generates an anomalous dephasing scaling as , establishing a falsifiable target for the space-based LISA observatory.