How does spacetime curvature explain gravity?

In general relativity, gravity is not a traditional pulling force, but rather the natural result of spacetime being curved by mass and energy. Objects move along natural curved paths called geodesics determined by local geometry. The metric tensor acts as the fundamental geometric tool capturing this structure and replacing classical gravitational potentials.

What we know

• Curved spacetime is the mathematical model in general relativity where gravity naturally arises instead of acting as a fundamental force in a static Euclidean frame. [2]
• Objects move along geodesics, which are curved paths determined by the local geometry of spacetime rather than being pulled by distant bodies. [2]
• The metric tensor captures the geometric and causal structure of spacetime, defining time, distance, volume, curvature, and angle. [3]
• The metric tensor plays the role of the gravitational potential from classical gravitation theory within general relativity. [3]

Where to go next

• how it workedWhat is a metric tensor in general relativity?
• what followedHow do geodesics explain particle motion?
• what caused itWhat are Einstein's field equations?
• compared withHow does Newtonian gravity compare to general relativity?
• the bigger pictureWhat role do spacetime symmetries play in solving physics problems?
• an unexpected connectionHow do spacetime symmetries simplify solving Einstein's equations?Although spacetime curvature describes gravity dynamically, exploiting symmetries helps physicists solve exact solutions to those very same equations.

Sources

• [1]spacetime curvature (Wikidata Q4240689) · CC0 1.0
• [2]Curved spacetime · CC BY-SA 4.0
• [3]Metric tensor (general relativity) · CC BY-SA 4.0
• [4]Mathematics of general relativity · CC BY-SA 4.0
• [5]Spacetime symmetries · CC BY-SA 4.0

Your path

1. What are Mount Manengouba and other stratovolcanoes like?
2. /How does spacetime curvature explain gravity?