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Notes on General Relativity

Einstein's Modified Field Equations :
This set of 10 equations (coupled, nonlinear, hyperbolicelliptic partial differential equations) in general relativity describes the fundamental interaction of gravity as a result of spacetime being curved by matter and energy.
Ruv (Ricci Curvature Tensor) and g (the Metric Tensor of our Universe) pertain to the structure of spacetime.
R, the Ricci scalar or scalar curvature, measures the deviation from Euclidean space in a curved Riemannian manifold.
Tuv (StressEnergyMomentum Tensor) describes the energy and flux of energy and momentum in spacetime. As the source of the gravitational field, Tuv is an attribute of matter, radiation and nongravitational force fields.
∧ is the Cosmological Constant, with the same effect as an intrinsic energy density of the vacuum. Its empirical positive value implies a positive pressure driving an accelerating expansion of empty space, thus the Universe.
Drafted by Stewart Yeung on 4 Feb 2012
