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The harmonic coordinate condition is one of several coordinate conditions in general relativity, which make it possible to solve the Einstein field equations...

fixing. Thus, coordinate conditions are a type of gauge condition. No coordinate condition is generally covariant, but many coordinate conditions are...

covariant derivative General covariant transformations Harmonic coordinate condition Inertial frame of reference Lorentz covariance Principle of covariance...

formally precise statement of the condition, it is necessary to define the following quantities: Spatial coordinate: one of the coordinates of the physical...

relativity by Albert Einstein and Cornelius Lanczos (see harmonic coordinate condition). Following the work of Dennis DeTurck and Jerry Kazdan in 1981,...

In geometry, curvilinear coordinates are a coordinate system for Euclidean space in which the coordinate lines may be curved. These coordinates may be...

spacetime coordinate system relative to an implied observer. In many (but not all) coordinate systems, an event is specified by one time coordinate and three...

time evolution of the metric tensor. It must be combined with a coordinate condition, which is analogous to gauge fixing in other field theories. To understand...

circular algebraic curves. Just as the selection of axes in the Cartesian coordinate system is somewhat arbitrary, the selection of a single system of homogeneous...

geographic coordinate systems is made necessary by the different geographic coordinate systems in use across the world and over time. Coordinate conversion...

invariance of the form of physical laws under arbitrary differentiable coordinate transformations, which is an important idea in general relativity. Invariance...

A projected coordinate system – also called a projected coordinate reference system, planar coordinate system, or grid reference system – is a type of...

no-slip condition is a boundary condition which enforces that at a solid boundary, a viscous fluid attains zero bulk velocity. This boundary condition was...

In mathematics, the real coordinate space or real coordinate n-space, of dimension n, denoted Rn or R n {\displaystyle \mathbb {R} ^{n}} , is the set...

In mathematics and mathematical physics, a coordinate basis or holonomic basis for a differentiable manifold M is a set of basis vector fields {e1, .....

The principal invariants of tensors do not change with rotation of the coordinate system (see Invariants of tensors). The singular values of a matrix are...

on the basis. One also says that the n-tuple of the coordinates is the coordinate vector of v on the basis, since the set F n {\displaystyle F^{n}} of the...

evolving variables, which together can be denoted by an n-dimensional coordinate vector), generally nk initial conditions are needed in order to trace...

dk_{x}\,dk_{y}\,.} At this point another coordinate transformation can be proposed (i.e., the Abbe sine condition) relating the object plane wavenumber spectrum...

In geometry, a barycentric coordinate system is a coordinate system in which the location of a point is specified by reference to a simplex (a triangle...