General Relativity

The general-relativity category develops the classical relativistic theory of gravity from explicit postulates and mathematical definitions: the smooth time-oriented Lorentzian geometry of the framework, tensors and observers, connections and free fall, curvature and tides, the Einstein field law and its matter branches, local and global energy, the flat and Newtonian bridges, the spherical vacuum and cosmological models, linearized waves, causal and initial-value structure, and the experimental interface. Physical postulates are adopted assumptions of a model; the mathematical results of the category are complete conditional deductions from those postulates and stated hypotheses, and no theorem establishes that the model describes nature. Curvature, geodesic and field-equation claims are always relative to a specified smooth model and its matter content, with the smooth-branch and regularity restrictions stated on the page where they are used. Empirical comparisons are recorded only with source-backed observations, apparatus and uncertainty qualifications; agreement of predictions with observations is evidence about the combined model and apparatus assumptions, not a proof of the postulates.