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Einstein field equations
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Relate geometry to energy and momentum.
G_μν = 8πG T_μν/c⁴G_μν = 8πG T_μν/c⁴ relates curvature (left) to the energy-momentum distribution (right). Their solutions include black holes, gravitational waves and expanding universes.
Ten coupled nonlinear equations.
Highly nonlinear, so exact solutions are rare.
In more detail
The Einstein field equations relate the curvature of spacetime to the distribution of mass and energy. They are a set of nonlinear partial differential equations at the heart of general relativity.
Real-world uses
- Physicists use them to model black holes and gravitational waves.
- Cosmologists use them to describe the expansion of the universe.
- Physicists solve Einstein's field equations to model black holes, neutron stars and the expansion of the universe.
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Frequently asked questions
Are they hard to solve?
Yes, they are nonlinear, and exact solutions exist only for special symmetric cases.
What does the left side describe?
The curvature of spacetime, through the Einstein tensor.
What do the equations relate?
The curvature of spacetime on one side and the energy and momentum of matter and fields on the other.
Related topics in Relativity
Gravitational redshift · GPS and relativity · Curved spacetime · Geodesics · Schwarzschild metric · Black hole event horizon