Explore black hole physics through the LFM framework. Calculate Schwarzschild radius, Hawking radiation, evaporation time, and see how LFM's χ field resolves the singularity problem.
Classical GR Problem: At r = 0, curvature → ∞, physics breaks down
LFM Solution: The χ field has a Mexican hat self-interaction V(χ)=λH(χ²−χ₀²)² that provides a stable Z₂ vacuum at −χ₀, preventing singularities
// GOV-02: χ field equation
∂²χ/∂t² = c²∇²χ − κ(Σ|Ψ|² − E₀²)
− 4λH·χ(χ²−χ₀²) ← Mexican hat!
BH interior: χ → −χ₀ (Z₂ vacuum)
The χ field depression around the black hole. At the event horizon (r = r_s), χ = 0 and light cannot escape. As you move away, χ recovers toward χ₀.
Red dashed line = event horizon (r = r_s). Purple dashed line = vacuum value (χ₀ = 19)
This black hole's tidal forces at the horizon are survivable! A human could cross the event horizon without being stretched apart.
Tidal acceleration difference across 1m: 5.980e-4 m/s²
Human lethal threshold: ~10× body gravity = ~100 m/s²
// Schwarzschild radius
r_s = 2GM/c²
// Hawking temperature
T_H = ℏc³/(8πGMk_B)
// Evaporation time
τ = 5120πG²M³/(ℏc⁴)
// LFM χ profile
χ(r)/χ₀ = √(1 - r_s/r)
// Mexican hat self-interaction (GOV-02 v14)
V(χ) = λ_H(χ²−χ₀²)², λ_H = 4/31 → Z₂ vacuum at χ = −19
// Bekenstein entropy
S = c³A/(4Gℏ)