Einstein's Equations
One of the core ideas of general relativity is that the metric (and the associated geometry of spacetime) is determined by the matter and energy content of spacetime. Einstein's field equations:
where
relate the metric (and the associated curvature tensors) to the stress-energy tensor . This tensor equation is a complicated set of nonlinear partial differential equations for the metric components. Exact solutions of Einstein's field equations are very difficult to find.
Read more about this topic: Metric Tensor (general Relativity)
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“In so far as the statements of geometry speak about reality, they are not certain, and in so far as they are certain, they do not speak about reality.”
—Albert Einstein (1879–1955)