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In general relativity, four-dimensional vectors, or four-vectors, are required. These four dimensions are length, height, width and time. A "point" in this context would be an event, as it has both a location and a time. Similar to vectors, tensors in relativity require four dimensions. One example is the Riemann curvature tensor.
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. Novel techniques developed by numerical relativity ...
Relativity links mass with energy, and energy with momentum. The equivalence between mass and energy, as expressed by the formula E = mc 2, is the most famous consequence of special relativity. In relativity, mass and energy are two different ways of describing one physical quantity.
Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity between them (special relativity), or a difference in gravitational potential between their locations (general relativity). When unspecified, "time dilation" usually refers to the effect due to velocity.
Fig 2-2 Minkowski diagram for various speeds of the primed frame, which is moving relative to the unprimed frame. The dashed lines represent the light cone of a flash of light at the origin. The term Minkowski diagram refers to a specific form of spacetime diagram frequently used in special relativity.
General relativity has acquired a reputation as a theory of extraordinary beauty. [2] [19] [20] Subrahmanyan Chandrasekhar has noted that at multiple levels, general relativity exhibits what Francis Bacon has termed a "strangeness in the proportion" (i.e. elements that excite wonderment and surprise).
The following notations are used very often in special relativity: Lorentz factor = where = and v is the relative velocity between two inertial frames.. For two frames at rest, γ = 1, and increases with relative velocity between the two inertial frames.
In this regard, string theory can be seen as building on the insights of the Kaluza–Klein theory, in which it was realized that applying general relativity to a 5-dimensional universe, with one space dimension small and curled up, looks from the 4-dimensional perspective like the usual general relativity together with Maxwell's electrodynamics.