Astrophysics, Cosmology & Relativity

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 Joules or MeV / GeV

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) kg·m/s or GeV/c

Astrophysics, Cosmology & Relativity

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) Seconds (Time Interval)

Astrophysics, Cosmology & Relativity

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_☉) Meters or Kilometers

Astrophysics, Cosmology & Relativity

A region in spacetime where gravitational curvature and density become infinite, causing classical general relativity equations to break…

Lim (r → 0): R_μνρσ R^μνρσ → ∞ Infinite Curvature / Density

Astrophysics, Cosmology & Relativity

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) 4D Manifold (3 Space + 1 Time)

Astrophysics, Cosmology & Relativity

Albert Einstein's 1905 theory describing the physical behavior of space and time for observers moving in uniform non-accelerated inertial…

E² = (p c)² + (m₀ c²)², γ = 1 / √(1 - v²/c²) Theoretical Framework

Astrophysics, Cosmology & Relativity

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) Nuclear Energy & Abundances

Astrophysics, Cosmology & Relativity

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_☉ 10⁴⁴ Joules (Energy Output)

Astrophysics, Cosmology & Relativity

A famous thought experiment in special relativity where one twin travels into space at high speed and returns younger than the twin who…

τ_traveler = τ_stay / γ (Asymmetric acceleration worldlines) Years (Elapsed Proper Time)

Astrophysics, Cosmology & Relativity

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) M_☉ (Mass) or R_Earth (Radius)

Astrophysics, Cosmology & Relativity

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) Einstein-Rosen Bridge Topology