General Relativity Visualizer
A laboratory for curved spacetime

Matter tells space how to bend.
Space tells matter how to move.

Four pictures of Einstein's geometry of gravity. Each one takes a single idea and lets you push on it until the math turns into intuition. No formulas to memorize, just the shapes the equations make.

7
modules online
c = 1
geometric units
RK4
orbit integrator
60 fps
live target
Built for desktop and tablet. The shader-heavy modules run on the GPU and will slow on phones, which is a stated trade, not a bug.
v1.0 · webgl + three r128
Marty Math Free tools and simulations to help you explore the ideas behind the math, from chaos and fractals to the calculators that run the numbers on the decisions that matter. See all the tools.
mass1.00 M☉
bodies3
well depth0.00
staterunning
dragorbit·wheelzoom
Module 01 · Curvature

Curved spacetime

A mass dents a flat sheet, and the marbles roll along the straightest path it allows. No force pulls them; the curve is the gravity.

central mass1.0
orbiting bodies
The rubber sheet A real spacetime curves in four dimensions you cannot draw. The honest part of this picture is that the marbles follow a geodesic, not any force.
mass10 M☉
rₛ29.5 km
shadow2.6 rₛ
photon1.5 rₛ
dragtilt view·wheelzoom
Module 02 · Strong field

The black hole

Light bends along the curvature, and near the horizon it lifts the disk's far side into view above the shadow.

mass10 M☉
disk inclination68°
scenario
The shadow The dark disk reads wider than the horizon: it is the photon sphere, the radius where light itself can orbit, projected toward your eye.
modelEinstein
orbits0
drift0.0°
rate / orbit0.00°
ecc0.00
wheelzoom·dragpan
Module 03 · Comparative gravity

The precessing orbit

Newton draws the same ellipse forever. Relativity turns its long axis a touch each lap, tracing a slow rosette.

relativistic strength0.030
launch speed0.78
model
Mercury's 43 arcseconds For the real Mercury the drift is only 43 arcseconds per century, far too little to see here. Explaining it was general relativity's first triumph.
separation0.000
freq0 Hz
strain h0.0e-21
cycles0
phaserunning
Module 04 · Spacetime radiation

Gravitational waves

Two bodies circle and shake spacetime, leaking energy into ripples. The strip below is the chirp they radiate.

total mass65 M☉
mass ratio0.83
source
The chirp As the orbit tightens, the wave's pitch and volume climb together. That rising inspiral sweep encodes the masses, and LIGO first caught one in 2015.
spin a/M0.900
horizon1.436 M
ergosphere2.00 M
drag ωₘ0.000
wheelzoom·dragpan
Module 05 · Rotating spacetime

The Kerr black hole

A spinning mass does not just curve spacetime, it twists it. Inside the ergosphere ring, space is dragged so hard that nothing can hold still.

spin a / M0.900
test particles
Frame dragging Inside the ergosphere nothing can stay at rest relative to the distant stars, however hard it fires its engines. Space drags it around with the hole.
gravity0.707×
velocity0.436×
slowest0.436×
reference0.0 s
Module 06 · Proper time

Time dilation lab

Time is not the same for everyone. A deep gravity well and high speed each slow a clock; watch the right two lag.

well depth r / rₛ2.00
speed v / c0.90
scenario
Why GPS needs Einstein The two effects fight each other. A GPS satellite sits higher, so its clock runs faster, while its speed slows it; gravity wins by 38 microseconds a day.
emit λ450 nm
seen λ936 nm
redshift z1.082
freq kept0.480
leftdeep in the well·rightfar observer
Module 07 · Climbing out

Gravitational redshift

A photon does work to climb out of a gravity well and pays with its energy. It cannot slow, so it stretches and reddens.

emission depth r / rₛ1.30
emitted color
Pound and Rebka, 1960 The shift is tiny in everyday gravity. Pound and Rebka measured it for gamma rays climbing a 22.5 meter tower, exactly as Einstein predicted.