Astrophysics, Cosmology & Relativity — 60 Terms Defined

Relativistic Kinetic Energy Astrophysics, Cosmology & Relativity Joules or MeV / GeV The work required to accelerate a massive particle from rest to a relativistic velocity v. E_k = (γ - 1) m₀ c² = E_total - m₀ c²

Relativistic Momentum Astrophysics, Cosmology & Relativity kg·m/s or GeV/c The linear momentum of an object moving at relativistic speeds, scaled by the Lorentz factor γ. p = γ m₀ v = m₀ v / √(1 - v²/c²)

Relativistic Time Dilation Astrophysics, Cosmology & Relativity Seconds (Time Interval) The phenomenon where time passes slower for a clock in relative motion compared to a stationary observer's reference clock. Δt = γ Δt₀ = Δt₀ / √(1 - v²/c²)

Schwarzschild Radius Astrophysics, Cosmology & Relativity Meters or Kilometers The physical radius defining the event horizon of a non-rotating, spherically symmetric black hole of mass M. R_s = 2 G M / c² ≈ 2.95 km × (M / M_☉)

Singularity Astrophysics, Cosmology & Relativity Infinite Curvature / Density A region in spacetime where gravitational curvature and density become infinite, causing classical general relativity equations to break down. Lim (r → 0): R_μνρσ R^μνρσ → ∞

Spacetime Continuum Astrophysics, Cosmology & Relativity 4D Manifold (3 Space + 1 Time) A 4D mathematical continuum combining 3D space and 1D time into a unified pseudo-Riemannian manifold. ds² = g_μν dx^μ dx^ν (4D Pseudo-Riemannian Manifold)

Special Relativity Astrophysics, Cosmology & Relativity Theoretical Framework Albert Einstein's 1905 theory describing the physical behavior of space and time for observers moving in uniform non-accelerated inertial frames. E² = (p c)² + (m₀ c²)², γ = 1 / √(1 - v²/c²)

Stellar Nucleosynthesis Astrophysics, Cosmology & Relativity Nuclear Energy & Abundances The collective nuclear fusion reactions inside stars that synthesize heavier chemical elements from lighter primordial hydrogen and helium. 3 α → ¹²C (Triple-Alpha Process at T ~ 10⁸ K)

Supernova Astrophysics, Cosmology & Relativity 10⁴⁴ Joules (Energy Output) A catastrophic stellar explosion marking the death of a star, briefly outshining an entire galaxy and dispersing heavy elements into space. Type Ia: M = M_Ch; Type II: Core Collapse M > 8 M_☉

Twin Paradox Astrophysics, Cosmology & Relativity Years (Elapsed Proper Time) A famous thought experiment in special relativity where one twin travels into space at high speed and returns younger than the twin who stayed on Earth. τ_traveler = τ_stay / γ (Asymmetric acceleration worldlines)

White Dwarf Astrophysics, Cosmology & Relativity M_☉ (Mass) or R_Earth (Radius) The dense stellar remnant remaining after a low-to-medium mass star exhausts its core nuclear fuel and sheds its outer layers. P_deg ∝ ρ^(5/3) (Electron Degeneracy Pressure)

Wormhole Astrophysics, Cosmology & Relativity Einstein-Rosen Bridge Topology A hypothetical topological feature of spacetime creating a shortcut connecting two separate points in space and time. ds² = -c² dt² + dl² + (r₀² + l²) (dθ² + sin²θ dφ²)