Einstein’s Field Equations: The Math Behind Gravity

Einstein’s field equations are the core of general relativity, published in 1915.
They describe how matter and energy tell spacetime how to curve.
The curvature of spacetime then tells matter how to move.
The equations are tensor-based, making them valid in any coordinate system.
The stress-energy tensor encodes energy, momentum, pressure, and stress.
The solutions to the equations include black holes, expanding universes, and gravitational waves.
The Schwarzschild solution was the first exact black hole metric.
The equations predicted gravitational lensing, later confirmed by observations.
Even GPS satellites rely on corrections from Einstein’s field equations for accuracy.
At their heart, these equations reveal gravity as geometry, not force.