Einstein Field Equations -- from Eric Weisstein's World of Physics

Einstein Field Equations

Portions of this entry contributed by Thomas Mulligan

The gravitational effects produced by a given mass are described in general relativity by 16 coupled hyperbolic-elliptic nonlinear partial differential equations, called the Einstein field equations. As result of the symmetry of and , the actual number of equations reduces to 10, although there are an additional four differential identities (the Bianchi identities Eric Weisstein's World of Math) satisfied by , one for each coordinate.

The Einstein field equations are given by

(1)

where is the stress-energy tensor, and

(2)

is the Einstein tensor, Eric Weisstein's World of Math with the Ricci curvature tensor Eric Weisstein's World of Math, the metric tensor, and R the scalar curvature. Eric Weisstein's World of Math The nonlinearity of the Einstein field equations stems from the fact that masses affect the very geometry of the space in which they dwell. And this is the fundamental insight of (1): mass curves the geometry of spacetime, and the geometry of spacetime in turn tells masses how to move.

Brans-Dicke Theory, Cosmological Constant, Cosmological Equations, General Relativity, Schwarzschild Black Hole, Schwarzschild Black Hole--Constant Density

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