Spacetime curvature is the bending of spacetime’s geometry caused by the presence of mass and energy, and it is what general relativity identifies as the true source of gravity. Rather than treating gravity as a force pulling objects toward each other, general relativity treats it as objects simply following the straightest available paths through a spacetime that has been warped by nearby matter.
The amount of curvature at any point is governed by Einstein’s field equations, which relate the curvature directly to how much matter and energy are present there. More mass concentrated in a smaller region produces sharper curvature, which is why the spacetime near a black hole is curved far more severely than the spacetime near a planet.
Curvature is also two-way: matter tells spacetime how to curve, and that curvature in turn tells matter how to move, a relationship often summarised as Einstein’s central insight into gravity.
One everyday, observable sign of spacetime curvature is the ocean tide. The moon’s gravity curves spacetime slightly more strongly on the side of Earth facing it than on the far side, and that difference stretches the Earth and its oceans just enough to raise a bulge of water on both the near and far sides at once. The same underlying physics, magnified enormously, is what would tear an object apart falling into a black hole, since the curvature there changes so sharply over such a short distance that an object’s near side and far side experience wildly different gravitational pulls. Tidal forces are, in a real sense, curvature made physically felt, direct evidence that gravity is not simply a uniform pull but a genuine distortion of the geometry of spacetime itself.
Physicists often summarize this relationship with a single compact equation, sometimes paraphrased as ‘spacetime tells matter how to move, matter tells spacetime how to curve,’ a phrase coined by physicist John Archibald Wheeler that has become one of the most quoted one-line descriptions of general relativity ever written.