Spacetime curvature simulation
In general relativity gravity is not a force pulling through space; mass and energy curve spacetime, and objects follow the straightest possible paths through that curved geometry. This view lets you dial the mass and see the curvature respond.
Interactive, free and runs in your browser. Part of the General Relativity simulations.
What you will see
A grid of spacetime dips into a well around the central mass. As the mass grows the well deepens and steepens, and the critical radii appear: the event horizon at r = 2GM/c², from which nothing escapes, and the photon sphere at 1.5 times that, where light can orbit.
Try this
- Slide the mass up and watch how quickly the well steepens near the centre.
- Compare how far out the grid is affected at low and high mass.
- Find the photon sphere and the horizon, and check their ratio is 1.5.
Common misconception
The rubber-sheet picture is a helpful cartoon, not the theory: it uses gravity to explain gravity. What is curved is spacetime, and the curvature of time is responsible for most of everyday gravity.
Exam-style question
What is the Schwarzschild radius of the Sun (M = 1.99 × 10³⁰ kg)?
r_s = 2GM/c² = 2 × 6.67 × 10⁻¹¹ × 1.99 × 10³⁰ / (3.00 × 10⁸)² ≈ 2.95 × 10³ m. The Sun would have to be squeezed into a ball about 3 km across to become a black hole.
Key equations
r_s = 2GM / c²r_ph = 1.5 r_s
Curriculum
Enrichment beyond A-level, IB Physics A.5.