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Four-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space ... Einstein's theory of relativity is formulated in 4D space, [3] ...
In 1908, Hermann Minkowski presented a geometric interpretation of special relativity that fused time and the three spatial dimensions into a single four-dimensional continuum now known as Minkowski space. This interpretation proved vital to the general theory of relativity, wherein spacetime is curved by mass and energy.
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.
Higher-dimensional Einstein gravity is any of various physical theories that attempt to generalise to higher dimensions various results of the well established theory of standard (four-dimensional) Albert Einstein's gravitational theory, that is, general relativity.
Albert Einstein, physicist, 1879-1955, Graphic: Heikenwaelder Hugo,1999. Special relativity is a theory of the structure of spacetime. It was introduced in Einstein's 1905 paper "On the Electrodynamics of Moving Bodies" (for the contributions of many other physicists and mathematicians, see History of special relativity).
In the rigorous mathematical formulation of special relativity, we suppose that the universe exists on a four-dimensional spacetime M. Individual points in spacetime are known as events; physical objects in spacetime are described by worldlines (if the object is a point particle) or worldsheets (if the object is larger than a point).
Einstein manifolds in four Euclidean dimensions are studied as gravitational instantons. If M {\displaystyle M} is the underlying n {\displaystyle n} -dimensional manifold , and g {\displaystyle g} is its metric tensor , the Einstein condition means that
As spacetime is assumed to be four-dimensional, each index on a tensor can be one of four values. Hence, the total number of elements a tensor possesses equals 4 R , where R is the count of the number of covariant ( b i ) {\displaystyle (b_{i})} and contravariant ( a i ) {\displaystyle (a_{i})} indices on the tensor, r + s {\displaystyle r+s ...