Black Hole Simulator

Schwarzschild Spacetime — Interactive General Relativistic Physics Engine

Explore the extreme physics of black holes: event horizons, gravitational lensing, accretion disks, relativistic time dilation, and orbital mechanics — all modeled from Einstein's general theory of relativity.

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Event Horizon

Visualize the boundary from which nothing — not even light — can escape.

Gravitational Lensing

Watch light bend around the photon sphere, producing Einstein rings.

Accretion Disk

Temperature-graded disk of infalling matter, glowing at millions of degrees.

Time Dilation

See how clocks slow down near the event horizon — an extreme relativistic effect.

Schwarzschild Metric

The exact vacuum solution to Einstein's field equations for a spherical mass

The Schwarzschild metric describes spacetime geometry outside a non-rotating, uncharged spherical mass. It is the exact solution to Einstein's field equations in vacuum:

Line element in Schwarzschild coordinates

Schwarzschild radius — event horizon boundary

For the Sun: Rs ≈ 3 km. For a 10 M☉ black hole: Rs ≈ 30 km. For Sgr A* (4×10⁶ M☉): Rs ≈ 12 million km ≈ 0.08 AU.

Key Orbital Radii

Characteristic length scales in Schwarzschild spacetime

r = 0Singularity

Point of infinite density. Spacetime curvature diverges.

r = RsEvent Horizon

Boundary of no return. Escape velocity = c.

r = 1.5 RsPhoton Sphere

Unstable circular orbits for photons. Light can orbit the black hole.

r = 2 RsMarginally Bound Orbit

Lowest energy parabolic orbit. Just barely escapes if given an impulse.

r = 3 RsISCO

Innermost Stable Circular Orbit. Inside this, all orbits spiral inward.

Gravitational Time Dilation

Clocks run slower in stronger gravitational fields

From the Schwarzschild metric, a stationary clock at radius r ticks slower than a clock at infinity:

10 Rs

0.949

5.1% slower

2 Rs

0.707

29.3% slower

1.1 Rs

0.302

69.8% slower

For a circular orbit, the combined GR effect is: dτ/dt = √(1 − 3Rs/2r), with time freezing at the photon sphere (r = 1.5Rs).

Gravitational Lensing

Light deflection by spacetime curvature — Einstein's prediction

Light follows null geodesics — curved paths in curved spacetime. The deflection angle for a ray with impact parameter b is:

Weak-field Einstein deflection formula

Critical impact parameter — photons with b ≤ b_c are captured

Einstein ring radius (observer at D_L)

Accretion Disk Physics

Shakura-Sunyaev thin disk model

Infalling matter forms a rotating disk. The temperature profile of a thin (Shakura-Sunyaev) disk peaks at the ISCO and falls off with radius.

Stellar BH

T_peak ~ 10⁷ K

X-ray binary

Supermassive BH

T_peak ~ 10⁵ K

AGN / Quasar

Eddington luminosity — maximum stable accretion rate

Orbital Mechanics

Particle trajectories in Schwarzschild spacetime

The effective potential for a massive particle in Schwarzschild geometry includes a GR correction term that destabilizes orbits inside the ISCO:

The last term (GR correction) creates an unstable maximum at r = 3Rs, defining the ISCO as the innermost stable orbit.

Circular orbit velocity in Schwarzschild coordinates

Hawking Radiation

Quantum thermal emission from the event horizon (Hawking 1975)

Black holes are not perfectly black. Quantum field theory in curved spacetime predicts that particle-antiparticle pairs created near the horizon allow one partner to escape — the black hole radiates as a perfect blackbody at the Hawking temperature.

10 M☉

T ≈ 6×10⁻⁹ K

Undetectable

10¹² kg

T ≈ 10¹² K

Evaporating now

Planck mass

T ≈ T_P

Explosive

Bekenstein-Hawking Entropy

Entropy proportional to horizon area — holographic principle

Black hole entropy is proportional to the event horizon area, not volume. This is the deepest hint of the holographic principle: information is encoded on a 2D surface.

where ℓ_P = √(Għ/c³) ≈ 1.616 × 10⁻³⁵ m (Planck length)

Evaporation timescale — for 10 M☉: ~2×10⁷⁴ years

Observed Black Hole Catalog

Confirmed black holes with observationally-measured masses. All values from peer-reviewed literature; click any row to load in the simulator.

Name	Type	Mass	Rs	Distance	Method / Reference
Cygnus X-1	Stellar	21.2 ± 2.2 M☉	~62.6 km	1.86 kpc	Stellar dynamics + parallax · Reid et al. 2011
GRS 1915+105	Stellar	12.4⁺²·⁰₋₁.₈ M☉	~36.6 km	8.6 kpc	Optical spectroscopy · McClintock et al. 2006
GW150914	Stellar (merger)	62⁺⁴₋₄ M☉	~183 km	410 Mpc	Gravitational waves (LIGO) · Abbott et al. 2016
GW190521	Intermediate (merger)	142⁺²⁸₋₁₆ M☉	~419 km	5.3 Gpc	Gravitational waves (LIGO/Virgo) · Abbott et al. 2020
Sgr A*	Supermassive	(4.154 ± 0.014) × 10⁶ M☉	~12.27 × 10⁶ km	8.277 kpc	Stellar orbits (S2) + VLBI · GRAVITY Collab. 2022
M87*	Supermassive	(6.5 ± 0.7) × 10⁹ M☉	~19.2 × 10⁹ km	16.8 Mpc	EHT imaging + stellar velocities · EHT Collaboration 2019
NGC 1277	Ultramassive	~1.7 × 10¹⁰ M☉	~5 × 10¹⁰ km	73 Mpc	Stellar kinematics · van den Bosch et al. 2012
TON 618	Ultramassive	6.6 × 10¹⁰ M☉	~1.95 × 10¹¹ km	10.4 Gpc	Reverberation mapping · Shemmer et al. 2004

Explore the Simulation

Interactively adjust black hole mass, accretion rate, and observer distance. Watch particles orbit, photons bend, and time dilate.

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