“Spacetime tells matter how to move; matter tells spacetime how to curve.”

The General Relativity Field Equations describe how matter and energy shape the geometry of spacetime and, in turn, how that curved spacetime governs motion. In compact form, Einstein’s equations link the distribution of mass, energy, pressure, and momentum to spacetime curvature. Gravity is no longer treated simply as a force pulling objects together; instead, planets, stars, and light follow paths through a warped geometric landscape. The equations predict phenomena such as black holes, gravitational waves, and the expansion of the universe. They are used primarily in astrophysics, cosmology, and gravitational physics.