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Caltech Tutorial on Relativity — A simple introduction to Einstein's Field Equations. The Meaning of Einstein's Equation — An explanation of Einstein's field equation, its derivation, and some of its consequences; Video Lecture on Einstein's Field Equations by MIT Physics Professor Edmund Bertschinger. Arch and scaffold: How Einstein found ...
The Einstein–Hilbert action in general relativity is the action that yields the Einstein field equations through the stationary-action principle.With the (− + + +) metric signature, the gravitational part of the action is given as [1]
In general relativity, an exact solution is a solution of the Einstein field equations whose derivation does not invoke simplifying assumptions, though the starting point for that derivation may be an idealized case like a perfectly spherical shape of matter.
Next, notice that only 10 of the original 14 equations are independent, because the continuity equation ; = is a consequence of Einstein's equations. This reflects the fact that the system is gauge invariant (in general, absent some symmetry, any choice of a curvilinear coordinate net on the same system would correspond to a numerically ...
Einstein's equations can also be solved on a computer using sophisticated numerical methods. [1] [2] [3] Given sufficient computer power, such solutions can be more accurate than post-Newtonian solutions. However, such calculations are demanding because the equations must generally be solved in a four-dimensional space.
In theoretical physics and applied mathematics, a field equation is a partial differential equation which determines the dynamics of a physical field, specifically the time evolution and spatial distribution of the field. The solutions to the equation are mathematical functions which correspond directly to the field, as functions of time and space.
The static assumption is unneeded, as Birkhoff's theorem states that any spherically symmetric vacuum solution of Einstein's field equations is stationary; the Schwarzschild solution thus follows. Birkhoff's theorem has the consequence that any pulsating star that remains spherically symmetric does not generate gravitational waves , as the ...
Albert Einstein's discovery of the gravitational field equations of general relativity and David Hilbert's almost simultaneous derivation of the theory using an elegant variational principle, [B 1]: 170 during a period when the two corresponded frequently, has led to numerous historical analyses of their interaction.