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From the explicit form of the Einstein tensor, the Einstein tensor is a nonlinear function of the metric tensor, but is linear in the second partial derivatives of the metric. As a symmetric order-2 tensor, the Einstein tensor has 10 independent components in a 4-dimensional space. It follows that the Einstein field equations are a set of 10 ...
General relativity. Lovelock's theorem of general relativity says that from a local gravitational action which contains only second derivatives of the four-dimensional spacetime metric, then the only possible equations of motion are the Einstein field equations. [1][2][3] The theorem was described by British physicist David Lovelock in 1971.
In the mid-1980s, a decade after Lovelock proposed his generalization of the Einstein tensor, physicists began to discuss the quadratic Gauss–Bonnet term within the context of string theory, with particular attention to its property of being ghost-free in Minkowski space. The theory is known to be free of ghosts about other exact backgrounds ...
Numerical relativity is the sub-field of general relativity which seeks to solve Einstein's equations through the use of numerical methods. Finite difference, finite element and pseudo-spectral methods are used to approximate the solution to the partial differential equations which arise.
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation ...
e. 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. Mathematically, finding an exact solution means finding a Lorentzian manifold ...
e. General relativity is a theory of gravitation developed by Albert Einstein between 1907 and 1915. The theory of general relativity says that the observed gravitational effect between masses results from their warping of spacetime. By the beginning of the 20th century, Newton's law of universal gravitation had been accepted for more than two ...
v. t. e. In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. [1] The equations were published by Albert Einstein in 1915 in the form of a tensor equation [2] which related the local spacetime curvature (expressed by ...