Three Fathoms Observatory
Stewart Yeung

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Studies

 

     

 

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  •     Notes on General Relativity

 

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    Einstein's Modified Field Equations :

     

    This set of 10 equations (coupled, nonlinear, hyperbolic-elliptic 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 (Stress-Energy-Momentum 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 non-gravitational 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