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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 ...
In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric vector [1] or spatial vector, [2] or – as here – simply a vector) is a geometric object that has both a magnitude (or length) and direction. A vector is what is needed to "carry" the point A to the point B; the Latin word vector means "one who carries ...
Fig 2-3 Different scales on the axes. The angle α between the x and x′ axes will be identical with that between the time axes ct and ct′. This follows from the second postulate of special relativity, which says that the speed of light is the same for all observers, regardless of their relative motion (see below). The angle α is given by [5]
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.
M-theory aims to unify quantum mechanics with general relativity's gravitational force in a mathematically consistent way. In comparison, other theories such as loop quantum gravity are considered by physicists and researchers to be less elegant, because they posit gravity to be completely different from forces such as the electromagnetic force.
The space R 3 is endowed with a scalar product , . Time is a scalar which is the same in all space E 3 and is denoted as t. The ordered set { t} is called a time axis. Motion (also path or trajectory) is a function r : Δ → R 3 that maps a point in the interval Δ from the time axis to a position (radius vector) in R 3.
Because general relativity predicts the inevitable occurrence of singularities, the theory is not complete without a specification for what happens to matter that hits the singularity. One can extend general relativity to a unified field theory, such as the Einstein–Maxwell–Dirac system, where no such singularities occur.
In the preface to Relativity: The Special and the General Theory, Einstein said "The present book is intended, as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical ...