relativity

What I do

• Analyze time dilation and length contraction
• Calculate relativistic momentum and energy
• Model spacetime diagrams and worldlines
• Study gravitational lensing and black holes
• Apply equivalence principle concepts
• Analyze cosmological metrics

When to use me

When studying high-speed phenomena, gravitational physics, or cosmology.

Key Concepts

• Lorentz Factor: γ = 1/√(1 - v²/c²) for time dilation and length contraction
• Mass-Energy Equivalence: E = mc², relativistic momentum p = γmv
• Spacetime Interval: ds² = -c²dt² + dx² + dy² + dz² (invariant)
• Einstein Field Equations: G_{μν} = (8πG/c⁴) T_{μν} relates geometry to matter
• Schwarzschild Metric: Describes spacetime outside spherical mass
• Gravitational Redshift: z = √((1-r_s/R)/(1-r_s/r)) - 1