🕳️ Black Hole Properties Calculator

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.

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🔬 LFM Insight: No Singularity

Classical GR Problem: At r = 0, curvature → ∞, physics breaks down

LFM Solution: The χ field has a floor term λ(−χ)³Θ(−χ) that prevents χ from going negative, ensuring spacetime remains well-behaved

// GOV-02: χ field equation

∂²χ/∂t² = c²∇²χ − κ(Σ|Ψ|² − E₀²)

+ λ(−χ)³Θ(−χ) ← Floor term!

χ ≥ χ_min > 0 always

📏Schwarzschild Radius
12259.63 thousand km
r_s = 2GM/c² = 1.226e+10 m
🌡️Hawking Temperature
1.49e-14 K (colder than CMB)
T_H = ℏc³/(8πGMk_B)
Evaporation Time
1.09e+77× universe age
Time until complete Hawking evaporation
⬇️Surface Gravity
3.666e+6 m/s²
3.737e+5 × Earth gravity
💡Hawking Luminosity
5.227e-42 W
Power output from Hawking radiation
📊Bekenstein Entropy
1.889e+113 bits
Maximum information content

🔮 LFM Predictions

χ at Event Horizon
χ = 0
Light cannot escape where χ = 0
χ Minimum (Floor)
2.362e-15 χ₀
Floor term prevents singularity
LFM Correction to T_H
~0 (negligible)
Significant only at Planck scale

χ Field Profile

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)

⚠️ Spaghettification

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

🎓 Key Physics

Standard GR Results

  • Schwarzschild radius: r_s = 2GM/c² (event horizon)
  • Hawking temperature: T ∝ 1/M (smaller = hotter)
  • Evaporation time: τ ∝ M³ (stellar BH: 10⁶⁷ years)
  • Bekenstein entropy: S ∝ A ∝ M² (holographic!)

LFM Additions

  • χ = 0 at horizon: Explains why light cannot escape
  • Floor term: χ ≥ χ_min prevents true singularity
  • Modified Hawking: Corrections at Planck scale
  • Information paradox: χ floor may preserve unitarity

Equations Used

// 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)

// Floor term (GOV-02)

λ(-χ)³Θ(-χ), λ = 10

// Bekenstein entropy

S = c³A/(4Gℏ)