Elastodynamic Geodesic Discontinuity Theory (EGST): A Curvature-Threshold Phenomenological Framework Compatible with General Relativity

Elastodynamic Geodesic Discontinuity Theory (EGST) is a phenomenological framework compatible with General Relativity (GR), developed by theoretically strengthening the Rubber Sheet Model and expanding the geometric-dynamic framework. Key features: fully compatible with GR, reducing to GR in low curvature regimes; D(x) = (1/Λ²)√(RμνρσRμνρσ) is an effective scalar derived from curvature invariants; effective metric defined as g_effμν = gμν + α D(x) hμν; geometric phase transition occurs when critical threshold D_c is exceeded; scale-dependent selectivity mechanism; qualitative alignment with dark matter observations. The theory begins by representing spacetime with the Rubber Sheet Model. In this model, massive objects move like objects on a rubber sheet creating depressions; the depth of the depression is directly proportional to the object's mass and inversely proportional to the sheet's elastic coefficient. As the universe expands, the natural depth of these depressions increases, meaning the sheet's elastic limits rise over time with cosmic expansion. A sudden pressure increase or local density change (such as a supernova, stellar explosion, or black hole formation) can cause a rapid increase in depth. If this sudden depth increase exceeds the sheet's elastic limit, a "geodesic discontinuity" (tear) occurs. This tear is not a physical hole but a geometric distortion of space, and theoretically can function as a wormhole opening to another dimension or different spacetime geometry. The term "another dimension" indicates that the tear's effect points to a possibility beyond normal spacetime; it is not observable, merely a mathematical and conceptual consequence of the model. The size of tears is limited by the mass that created them and the current depth of the sheet; due to cosmic expansion, tears cannot exceed the diameter of black holes. These tears are not directly observable; they can only be inferred indirectly by observing changes in the behavior of approaching objects. The selectivity mechanism of the theory operates as follows: Objects larger than the tear (planets, stars) cannot enter or get caught in the tear due to their size; they only change direction by grazing its edge (deflection). For objects smaller than the tear, their fate depends on velocity: if slow, they are pulled into the tear; if fast, the tear cannot capture them, and they either slightly alter course or pass through unaffected. The model provides a phenomenological framework with testable qualitative predictions: microlensing anomalies, gravitational wave phase shifts, critical curvature regime transition signatures, orbital distribution deviations, and statistical departures from GR in weak lensing observations.