| name | relativity-spacetime |
| description | Formulate and verify special- and general-relativity problems. Use for Lorentz transformations, four-vectors, relativistic kinematics, metrics, geodesics, curvature, gravitational fields, horizons, and stress-energy dynamics. |
| license | MIT |
Relativity and Spacetime
Fix conventions
Define events, observers, coordinates, units for c and G, metric signature, index placement, orientation,
curvature convention, and approximation regime. Separate coordinate quantities from locally measured
observables. Identify timelike, null, and spacelike intervals before manipulating velocities or paths.
For a purely Riemannian manifold with no spacetime interpretation, mark causal and c, G conventions as
not applicable and use $cx-tensor-calculus-differential-geometry as the primary workflow.
Select the model
- In special relativity, use Lorentz transformations, invariant intervals, four-velocity, and four-momentum.
- For collisions or decays, conserve four-momentum and use invariant masses before choosing a frame.
- In general relativity, state the metric and symmetries, then derive connections, geodesics, and curvature.
- Relate geometry to matter with an explicit stress-energy tensor and field-equation convention.
- Use weak-field, slow-motion, or post-Newtonian approximations only after declaring their dimensionless limits.
Verify
- Check invariant intervals, four-vector norms, index contractions, tensor transformation, and dimensions.
- Recover Newtonian or special-relativistic behavior in the appropriate limit.
- Verify metric compatibility, geodesic normalization, conserved quantities from Killing symmetries, and constraints.
- Distinguish coordinate singularities from curvature singularities using invariants or regular coordinates.
- Cross-check symbolic results numerically at nonsingular points and test causal character along trajectories.
Deliver
Report conventions, geometry or frame, equations, invariant observables, approximation order, checks, and
domains excluded by coordinates or model assumptions.
Source basis
Original synthesis informed by Crowell's openly licensed General Relativity and Modern Physics; source
details are in ../../docs/TEXTBOOK_SOURCES.md.
