Quantum & Black Hole Observatory

Quantum & Black Hole Observatory

Science Suite v1.0 · Real Physics · SI Units

LIVE SIMULATION

TriPod LLC · DLW

I. Black Hole — Schwarzschild Geometry

II. Quantum Wave Function ψ(x,t)

III. Bloch Sphere — Qubit State

IV. Spacetime Curvature (Flamm Paraboloid)

Black
Hole

Quantum
States

Thermodynamics

Constants

⬤ Schwarzschild Radius

r_s = 2GM/c²

Mass (solar masses M☉)

Mass input

Schwarzschild radius r_s—

Photon sphere r_ph—

ISCO (innermost stable orbit)—

Event horizon area A—

Surface gravity κ—

Mass (kg)—

✦ Hawking Radiation

T_H = ℏc³ / (8πGMk_B)

Hawking temperature T_H—

Peak wavelength λ_max—

Luminosity (power)—

Evaporation time t_evap—

B-H entropy S—

⏱ Gravitational Time Dilation

dt_local / dt_∞ = √(1 − r_s/r)

Observer distance from center (× r_s)

1.01 r_s (horizon)10 r_s100 r_s

Time ratio t_local/t_∞—

1 year at distance = ? years far—

Redshift z—

Escape velocity—

↕ Tidal Force (Spaghettification)

ΔF = 2GMmδr / r³

Body size δr (meters)

Body mass m (kg)

Tidal force at event horizon—

Tidal force at ISCO—

Spaghettification distance—

Survivable below M =—

🌀 Kerr Black Hole (Spin)

a* = Jc / (GM²) ∈ [0,1]

Spin parameter a* (0 = Schwarzschild, 1 = max Kerr)

0 (no spin)0.5001 (max)

Outer event horizon r+—

Inner event horizon r−—

Ergosphere radius (equator)—

ISCO (prograde)—

Frame dragging Ω—

Penrose process efficiency—

◎ Qubit State |ψ⟩ = α|0⟩ + β|1⟩

|α|² + |β|² = 1

Polar angle θ (0 = |0⟩, π = |1⟩)

0 = |0⟩π/4π = |1⟩

Azimuthal angle φ (phase)

002π

|ψ⟩ = —

α (|0⟩ amplitude)—

β (|1⟩ amplitude)—

P(|0⟩) measurement prob.—

P(|1⟩) measurement prob.—

Von Neumann entropy S—

△ Heisenberg Uncertainty

Δx · Δp ≥ ℏ/2

Position uncertainty Δx (meters)

Min. momentum uncertainty Δp—

Min. velocity uncertainty Δv (electron)—

Min. velocity uncertainty Δv (proton)—

Δx · Δp product—

ΔE · Δt ≥ ℏ/2

Time uncertainty Δt (seconds)

Min. energy uncertainty ΔE—

ΔE in eV—

⦿ Hydrogen Atom

E_n = −13.6 eV / n²

Principal quantum number n

Transition to level n'

Energy level E_n—

Bohr radius r_n—

Orbital speed v_n—

Transition energy ΔE—

Photon wavelength λ—

Spectral series—

⇢ Quantum Tunneling (WKB)

T ≈ exp(−2∫κ dx), κ = √(2m(V−E)/ℏ²)

Barrier width L (nm)

Barrier height V (eV)

Particle energy E (eV)

Transmission probability T—

Reflection probability R—

κ (decay constant)—

de Broglie λ outside barrier—

◈ Bekenstein–Hawking Entropy

S = k_BA / (4ℓ_p²) = 4πGM²k_B/(ℏc)

Entropy S (J/K)—

Entropy in Planck units—

Planck area quanta (bits)—

Holographic bound—

T dS = dM c² → First law of BH mechanics

dS/dM (entropy change per kg)—

Information content (Planck bits)—

★ Stellar Remnant Thresholds

Chandrasekhar limit (WD)1.4 M☉

TOV limit (neutron star)~2.2–2.9 M☉

Minimum BH mass (theory)~5 M☉

Stellar BH typical range5–100 M☉

Intermediate mass BH10² – 10⁵ M☉

Supermassive BH range10⁶ – 10¹⁰ M☉

Sgr A* (Milky Way center)4.15 × 10⁶ M☉

M87* (EHT observed)6.5 × 10⁹ M☉

∞ Planck Scale

Planck length ℓ_p1.616 × 10⁻³⁵ m

Planck time t_p5.391 × 10⁻⁴⁴ s

Planck mass m_p2.176 × 10⁻⁸ kg

Planck temperature T_p1.417 × 10³² K

Planck energy E_p1.956 × 10⁹ J

Planck charge q_p1.876 × 10⁻¹⁸ C

⚖ Mass → r_s Quick Reference

Sun (1 M☉)r_s = 2.95 km

Earth (1 M⊕)r_s = 8.87 mm

10 M☉r_s = 29.5 km

Sgr A* (4.15×10⁶ M☉)r_s ≈ 12.2 Gm

M87* (6.5×10⁹ M☉)r_s ≈ 19.2 Tm

Proton massr_s = 2.48 × 10⁻⁵⁴ m

π Fundamental Constants

GRAVITATIONAL / RELATIVISTIC

G6.674 × 10⁻¹¹ N·m²·kg⁻²

c2.998 × 10⁸ m·s⁻¹

M☉1.989 × 10³⁰ kg

M⊕5.972 × 10²⁴ kg

QUANTUM MECHANICS

ℏ1.055 × 10⁻³⁴ J·s

h6.626 × 10⁻³⁴ J·s

k_B1.381 × 10⁻²³ J·K⁻¹

e1.602 × 10⁻¹⁹ C

m_e9.109 × 10⁻³¹ kg

m_p1.673 × 10⁻²⁷ kg

a_05.292 × 10⁻¹¹ m (Bohr radius)

α1/137.036 fine-structure

PLANCK UNITS

ℓ_p1.616 × 10⁻³⁵ m

t_p5.391 × 10⁻⁴⁴ s

m_p2.176 × 10⁻⁸ kg

T_p1.417 × 10³² K

COSMOLOGICAL

H_067.4 km·s⁻¹·Mpc⁻¹

Λ1.089 × 10⁻⁵² m⁻²

ρ_c8.5 × 10⁻²⁷ kg·m⁻³

t_U13.787 × 10⁹ yr (universe age)

M = 10 M☉

r_s = —

T_H = —

a* = 0.500

TRIPOD-IP-v1.0 · DLW · TriPod LLC · 2026-02-18