In general relativity, the laws of physics can be expressed in a generally covariant form. In other words, the description of the world as given by the laws of physics does not depend on our choice of coordinate systems. However, it is often useful to fix upon a particular coordinate system, in order to solve actual problems or make actual predictions. A coordinate condition selects such coordinate system(s).
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fixing. Thus, coordinateconditions are a type of gauge condition. No coordinate condition is generally covariant, but many coordinateconditions are Lorentz...
The harmonic coordinate condition is one of several coordinateconditions in general relativity, which make it possible to solve the Einstein field equations...
In geometry, a Cartesian coordinate system (UK: /kɑːrˈtiːzjən/, US: /kɑːrˈtiːʒən/) in a plane is a coordinate system that specifies each point uniquely...
chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic nonlinear system...
groups, now play a major role in fundamental physical theories. CoordinateconditionsCoordinate-free Background independence Differential geometry Diffeomorphism...
In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be...
The horizontal coordinate system is a celestial coordinate system that uses the observer's local horizon as the fundamental plane to define two angles:...
constraints on the coordinate system in order to obtain unequivocal results. These constraints are known as coordinateconditions. A popular choice of...
determines a coordinate or coordinate block via a coordinate selection rule, then exactly or inexactly minimizes over the corresponding coordinate hyperplane...
the coordinateconditions. While physical effects cannot propagate from inside to outside, coordinate effects could. For example, if the coordinate conditions...
is called a coordinate singularity. As the name implies, the singularity arises from a bad choice of coordinates or coordinateconditions. When changing...
geographic coordinate systems is made necessary by the different geographic coordinate systems in use across the world and over time. Coordinate conversion...
solving this initial value problem requires selection of particular coordinateconditions. Spinors find several important applications in relativity. Their...
However, a recent derivation in 3 + 1 dimensions under the right coordinateconditions yields a formulation similar to the earlier 1 + 1, a dilaton field...
which together can be denoted by an n-dimensional coordinate vector), generally nk initial conditions are needed in order to trace the system's variables...
vector spaces based on different kinds of scalars: real coordinate space or complex coordinate space. Vector spaces generalize Euclidean vectors, which...
the velocity component to the corresponding coordinate z2). In each constraint equation, one coordinate is redundant because it is determined from the...
their own interests; controls multiple businesses, which intensively coordinate their activities. More generally, an oligarch (from Ancient Greek ὀλίγος...
called slab boundary conditions; in this case, PBCs are used for two Cartesian coordinates (e.g., x and y), and the third coordinate (z) extends to infinity...
latitude). Despite the physical dimension and unit of length, the vertical coordinate does not represent distance in physical space, as would be measured with...
transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity...
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