Finite-Response Coupled Field Dynamics (FRCFD) is a non-geometric framework in which gravity emerges from a finite-capacity substrate field rather than spacetime curvature. In weak-field regimes, the theory reproduces the leading-order predictions of General Relativity, while strong-field singularities are replaced by saturated, high-impedance cores, producing finite ISCO radii, photon spheres, and shadow sizes. Strong-field gravitational lensing and accretion disk observables provide independent constraints on the substrate response scale Smax, while cosmological redshift arises as a cumulative response effect that preserves the cosmic microwave background blackbody spectrum. This framework is fully falsifiable, with predictions testable via high-resolution imaging, X-ray spectroscopy, and cosmological surveys, and can be extended to rotating solutions and perturbative cosmology for a complete astrophysical and cosmological description. Finite-Response Coupled Field Dynamics: From A...
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Finite-Response Coupled Field Dynamics: From Accretion Disks to the Cosmic Microwave Background
Finite-Response Coupled Field Dynamics (FRCFD) is a non-geometric framework in which gravitational phenomena emerge from a finite-capacity substrate field, rather than from spacetime curvature. The theory reproduces General Relativity in weak-field regimes, while in strong-field environments, singularities are replaced by saturated, high-impedance cores that regulate response and prevent divergences. Finite-Response Coupled Field Dynamics: From Accretion Disks to the Cosmic Microwave Background March 20, 2026 Abstract We present Finite-Response Coupled Field Dynamics (FRCFD), a non-geometric framework in which gravitational phenomena arise from a finite-capacity substrate field rather than spacetime curvature. Matter sources a scalar response field S, whose finite response modifies propagation and clock rates through an exponential suppression function. The theory reproduces General Relativity (GR) to leading order in weak fields, while predicting measurable deviations in...
Finite-Response Coupled Field Dynamics: Strong-Field Predictions, Lensing, and Cosmological Constraints
10. Innermost Stable Circular Orbit (ISCO) in FRCFD March 20, 2026 Table of Contents (Section) 10.1 Timelike Motion in the Effective Metric 10.2 Conserved Quantities 10.3 Effective Potential 10.4 Circular Orbit Condition 10.5 Stability Criterion and ISCO 10.6 ISCO Radius 10.7 Comparison with General Relativity 10.8 Observational Constraints on Smax 10.9 Physical Interpretation 10.10 Limitations 10.11 Outlook 10.1 Timelike Motion in the Effective Metric Massive particle motion is described using the effective propagation metric: ds^2 = f(r)^2 dt^2 − f(r)^(−2) dr^2 − r^2 dΩ^2 We restrict to equatorial motion (θ = π/2) and define proper time τ for timelike trajectories (ds² > 0). 10.2 Conserved Quantities Stationarity and spherical symmetry imply conserved quantities: E = f(r)^2 (dt/dτ) L = r^2 (dφ/dτ) These constants fully determine orbital motion. 10.3 Effective Potential The normalization condition is: f(r)^...
Strong-Field Gravitational Lensing in FRCFD
11. Strong-Field Gravitational Lensing in FRCFD Table of Contents (Section) 11.1 Null Trajectories in the Response Metric 11.2 Impact Parameter 11.3 Deflection Angle (General Form) 11.4 Weak-Field Limit 11.5 Strong-Field Regime 11.6 Photon Sphere Connection 11.7 Observable Signatures 11.8 Constraints on Smax 11.9 Limitations 11.10 Outlook 11.1 Null Trajectories in the Response Metric Light propagation follows null trajectories (ds^2 = 0) in the effective metric: ds^2 = f(r)^2 dt^2 − f(r)^(−2) dr^2 − r^2 dΩ^2 Restricting to the equatorial plane: f(r)^2 (dt/dλ)^2 − f(r)^(−2) (dr/dλ)^2 − r^2 (dφ/dλ)^2 = 0 11.2 Impact Parameter Define conserved quantities: E = f(r)^2 dt/dλ L = r^2 dφ/dλ The impact parameter is: b = L / E Using the null condition: (dr/dλ)^2 = E^2 − f(r)^2 L^2 / r^2 11.3 Deflection Angle (General Form) The bending angle is: Δφ = 2 ∫ [dr / r^2] * [1 / sqrt(1/b^2 − f(r)^2 / r^2)] − π This expr...
Innermost Stable Circular Orbit (ISCO) in FRCFD
10. Innermost Stable Circular Orbit (ISCO) in FRCFD Table of Contents (Section) 10.1 Timelike Motion in the Effective Metric 10.2 Conserved Quantities 10.3 Effective Potential 10.4 Circular Orbit Condition 10.5 Stability Criterion and ISCO 10.6 Approximate ISCO Radius 10.7 Comparison with General Relativity 10.8 Observational Constraints on Smax 10.9 Physical Interpretation 10.10 Limitations 10.11 Outlook 10.1 Timelike Motion in the Effective Metric We analyze massive particle motion using the effective propagation metric: ds^2 = f(r)^2 dt^2 − f(r)^(−2) dr^2 − r^2 dΩ^2 For timelike geodesics (ds^2 > 0), we define proper time τ and restrict motion to the equatorial plane (θ = π/2). 10.2 Conserved Quantities Stationarity and spherical symmetry imply conserved energy and angular momentum: E = f(r)^2 dt/dτ L = r^2 dφ/dτ These constants fully determine orbital motion. 10.3 Effective Potential Using the normalization co...
FRCFD – Strong Field Predictions: Photon Sphere & Shadow
Finite-Response Coupled Field Dynamics (FRCFD): Strong-Field Predictions Table of Contents 1. Effective Propagation Framework 2. Canonical Response Function 3. Photon Sphere Derivation 4. Shadow Radius Prediction 5. Comparison with General Relativity 6. Physical Interpretation 7. Observational Implications 8. Limitations 9. Outlook 1. Effective Propagation Framework Within Finite-Response Coupled Field Dynamics (FRCFD), gravitational effects emerge from a scalar substrate field S(r), rather than spacetime curvature. The propagation of signals is described using an effective metric, which serves as a computational tool rather than a fundamental geometric object. ds^2 = f(S)^2 dt^2 − f(S)^(−2) dr^2 − r^2 dΩ^2 This metric encodes how finite response modifies time and radial propagation. The function f(S) represents the local response suppression of the substrate. 2. Canonical Response Function The theory adopts a unique and canonical resp...
Replacing Geometric Gravity with Saturation Physics and Impedance-Driven Cosmology
A Unified Response-Field Framework Replacing Geometric Gravity with Saturation Physics and Impedance-Driven Cosmology Finite-Response Coupled Field Dynamics (FRCFD) March 20, 2026 Table of Contents Abstract 1. Lagrangian & Field Equations 2. Canonical Response Function 3. Weak-Field Recovery 4. Strong-Field Structure 5. Observable Predictions 6. Energy Transfer & Conservation 7. Cosmology Without Expansion 8. Conclusion Abstract Finite-Response Coupled Field Dynamics (FRCFD) models relativistic phenomena as arising from a nonlinear substrate with finite response capacity. Time dilation, redshift, and gravitational effects are governed by a single response function: f(S) = exp(-S / Smax) All previous algebraic response forms should be interpreted as approximations; the exponential form is taken as canonical due to its smoothness and correct weak-field limit. Figure 1 Placeholder — Response function vs substrate stress 1. Lag...