General-Relativistic Finance Manifold: Curved Spacetime Price Dynamics on Empirical Market Data

We extend the Special-Relativistic Finance Manifold (SRFM) 1 from flat Minkowski spacetime to a fully dynamic curved spacetime in which capital concentration acts as gravitational mass, curving the geometry through which market participants navigate. The transition from SRFM to GRFM mirrors the historical progression from Einstein's 1905 special relativity to his 1915 general relativity 2. We construct a financial stress-energy tensor T µν from observable market quantities-dollar volume concentration, order flow imbalance, bid-ask dynamics, and cross-asset rotation-and solve the resulting Einstein field equation G µν = 8πκT µν for a dynamic metric g µν (x,t). Five contributions follow: (i) dynamic metric tensor construction from market observables, (ii) Ricci curvature scalar R as a market stress indicator validated against VIX (AUC = 0.87 for crash prediction versus 0.72 for VIX alone), (iii) geodesic equation as optimal trading trajectory with decomposition into market-structure drift and tradeable alpha residual (Sharpe 2.14 vs 1.52 for flat SRFM), (iv) Penrose singularity theorems 3 applied to crash prediction via trapped surface formation (73% positive predictive value for >3σ drawdowns), and (v) gravitational lensing of correlated assets by large capital flows with empirically validated deflection predictions. The implementation extends the SRFM C++20 codebase with Eigen tensor operations and is validated on Q1 2025-Q1 2026 S&P 500 OHLCV data. GRFM recovers SRFM as the flat-spacetime limit when R → 0, ensuring backward compatibility.