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If the energy–momentum tensor T μν is that of an electromagnetic field in free space, i.e. if the electromagnetic stress–energy tensor = (+) is used, then the Einstein field equations are called the Einstein–Maxwell equations (with cosmological constant Λ, taken to be zero in conventional relativity theory): + = (+).
In general relativity, this remaining precession, or change of orientation of the orbital ellipse within its orbital plane, is explained by gravitation being mediated by the curvature of spacetime. Einstein showed that general relativity [3] agrees closely with the observed amount of perihelion shift. This was a powerful factor motivating the ...
The Einstein field equations are nonlinear and considered difficult to solve. Einstein used approximation methods in working out initial predictions of the theory. But in 1916, the astrophysicist Karl Schwarzschild found the first non-trivial exact solution to the Einstein field equations, the Schwarzschild metric. This solution laid the ...
These amount to only 14 equations (10 from the field equations and 4 from the continuity equation) and are by themselves insufficient for determining the 20 unknowns (10 metric components and 10 stress–energy tensor components). The equations of state are missing. In the most general case, it's easy to see that at least 6 more equations are ...
In general relativity, an exact solution is a (typically closed form) solution of the Einstein field equations whose derivation does not invoke simplifying approximations of the equations, though the starting point for that derivation may be an idealized case like a perfectly spherical shape of matter.
The Einstein–Infeld–Hoffmann equations of motion, jointly derived by Albert Einstein, Leopold Infeld and Banesh Hoffmann, are the differential equations describing the approximate dynamics of a system of point-like masses due to their mutual gravitational interactions, including general relativistic effects.
The metric tensor is a central object in general relativity that describes the local geometry of spacetime (as a result of solving the Einstein field equations). Using the weak-field approximation, the metric tensor can also be thought of as representing the 'gravitational potential'. The metric tensor is often just called 'the metric'.
In general relativity, a scalar field solution is an exact solution of the Einstein field equation in which the gravitational field is due entirely to the field energy and momentum of a scalar field. Such a field may or may not be massless , and it may be taken to have minimal curvature coupling , or some other choice, such as conformal coupling .