Mathematics of General Relativity
An interactive journey through the mathematical foundations of Einstein's masterpiece - from tensors to the curvature of spacetime.
What is General Relativity?
General Relativity (GR), published by Albert Einstein in 1915, is our best theory of gravity. It describes gravity not as a force, but as the curvature of spacetime caused by mass and energy.
The mathematics of GR is built on differential geometry - the study of curved spaces. This site will guide you through the key mathematical concepts you need to understand Einstein's equations.
Key Insight
In GR, free-falling objects follow geodesics - the straightest possible paths through curved spacetime. What we perceive as gravitational attraction is actually the natural motion through curved geometry.
Interactive Visualization
Mass Curving Spacetime
Drag to rotate. Adjust mass to see how it warps the fabric of spacetime. The particle follows a geodesic orbit.
Explore the Mathematics
Tensor Calculus
The mathematical language of curved spaces - learn about contravariant and covariant tensors.
The Metric Tensor
How we measure distances and angles in curved spacetime.
Christoffel Symbols
Connection coefficients that describe how coordinate bases change.
Riemann Curvature
The mathematical measure of spacetime curvature.
Einstein Field Equations
The heart of GR - how matter curves spacetime.
Geodesics
The paths of free-falling objects through curved spacetime.
Black Holes
Event horizons, accretion disks, and the ultimate fate of collapsing matter.
Prerequisites
To fully appreciate the mathematics of GR, you should be familiar with:
- Multivariable Calculus - Partial derivatives, gradients, chain rule
- Linear Algebra - Matrices, vectors, transformations
- Special Relativity - Lorentz transformations, spacetime intervals
- Basic Physics - Newton's laws, classical mechanics
Don't worry if you're not an expert - we'll explain concepts as we go!