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Longer titles found: Metric tensor (general relativity) (view), Symmetric tensor (view), Antisymmetric tensor (view)

searching for Metric tensor 60 found (406 total)

alternate case: metric tensor

Synchronous frame (6,195 words) [view diff] no match in snippet view article find links to article

time coordinates with a beginning at the hypersurface. In terms of metric-tensor components g i k {\displaystyle g_{ik}} , a synchronous frame is defined

{\displaystyle g^{ij}} following the notation of the (contravariant) metric tensor in differential geometry. The Fisher information metric is denoted by

relativistic gravity, the gravitational field is described by the 10-component metric tensor. However, in Newtonian gravity, which is a limit of GR, the gravitational

{\displaystyle \eta _{\mu \nu }=\operatorname {diag} (-1,1,1,1)} is the metric tensor of Minkowski spacetime. The case where p=0 describes a dust solution

vector that is asymptotically timelike. In a stationary spacetime, the metric tensor components, g μ ν {\displaystyle g_{\mu \nu }} , may be chosen so that

five-dimensional Kaluza–Klein metric is the generalization of the four-dimensional metric tensor. It additionally includes a scalar field called graviscalar (or radion)

action of spacetime and then varying that action with respect to the metric tensor. The field equations of Einstein–Cartan theory come from exactly the

phenomenon that this solution model, but in terms of general relativity. The metric tensor of the unique exact solution modeling a linearly polarized electromagnetic

pmatrix}r_{x_{1}}\\r_{x_{2}}\\\vdots \\r_{x_{d}}\end{pmatrix}}} The metric tensor G {\displaystyle \mathbf {G} } is sometimes used for calculations involving

\;{\sqrt {-1\,}}\;} change the sign of the time-time components of the metric tensor.) The resulting functions are called Schwinger functions. For the Schwinger

Consider the covariant derivative of the density of the reciprocal of the metric tensor: 0 = ( g μ ν − g ) ; ρ = ( g μ ν − g ) , ρ + g σ ν Γ σ ρ μ − g + g μ

gravitational Lagrangian density, contains second derivatives of the metric tensor. This is a non-typical feature of field theories, which are usually

{s} ){\dot {S}}_{s}{\dot {S}}_{t},} where gst is an element of the metric tensor of the internal (curvilinear) coordinates. The dots indicate time derivatives

{s} ){\dot {S}}_{s}{\dot {S}}_{t},} where gst is an element of the metric tensor of the internal (curvilinear) coordinates. The dots indicate time derivatives

connection without making any explicit reference to any metric tensor (although the metric tensor can be understood to be a special case of a solder form

{\gamma }}\\\end{pmatrix}},} where g {\displaystyle \mathbf {g} } is the metric tensor expressed in Euler angles—a non-orthogonal system of curvilinear coordinates—

vanish. Here η μ ν {\displaystyle \eta _{\mu \nu }} is the Minkowski metric tensor. Additionally, D {\displaystyle D} is a scalar and K μ {\displaystyle

signature – Number of positive, negative and zero eigenvalues of a metric tensor Metric space – Mathematical space with a notion of distance Metrizable

second theory are conformally flat Lorentzian spacetimes. That is, the metric tensor can be written as g μ ν = A η μ ν {\displaystyle g_{\mu \nu }=A\eta

y−1 on an open subset of Euclidean space. The metric tensor relative to x is obtained from the metric tensor relative to y by a local calculation having

stress tensor of the boundary theory is the boundary value of the bulk metric tensor. In Rehren Duality, the bulk theory is an 'ordinary' (non-gravitational)

"composite boson", described by a "unimodular" (determinant 1) spatial metric-tensor field as the fundamental collective degree of freedom of Fractional

gravitational constant, g {\displaystyle g} is the determinant of the metric tensor g α β {\displaystyle g_{\alpha \beta }} , while Λ {\displaystyle \Lambda

kinetic energy. In general, the classical kinetic energy T defines the metric tensor g = (gij) associated with the curvilinear coordinates s = (si) through

\;\sigma ^{2}={\frac {1}{f(r)}}\,dr,\;\sigma ^{3}=rd\varphi } gives the metric tensor in terms of the same two undetermined functions: g = − σ 0 ⊗ σ 0 + σ

the Ricci scalar and g {\displaystyle g} is the determinant of the metric tensor. The scalar field Lagrangian is L s = − 1 2 [ σ 2 h α β ∂ α ϕ ∂ β ϕ

Cartesian chart on Minkowski spacetime, in the following sense. Write the metric tensor as the sum of a (physically unobservable) Minkowski background plus

} {\displaystyle g^{\mu \nu }={\rm {{diag}\{1,-1,-1,-1\}}}} is the metric tensor of the Minkowski space. Then, one can verify that both S {\displaystyle

"intrinsic" methods in linearized elasticity, where the linearized metric tensor and the linearized tensor of curvature change are the new, and only

self energy is noted Π ( q 2 ) {\displaystyle \Pi (q^{2})} and the metric tensor η μ ν {\displaystyle \eta ^{\mu \nu }} (here taking the +--- convention)

a vierbein, and, in particular, an orthonormal tetrad. That is, the metric tensor can be written as a pullback of the Minkowski metric η i j {\displaystyle

since, as shown in the BKL analysis itself, space-like gradients of the metric tensor cannot be neglected for generic solutions of pure Einstein gravity in

distance measurements; (2) must provide an alternative expression for the metric tensor in general relativity; (3) might contradict Lorentz invariance; (4)

a set of orthonormal space time vector fields that diagonalize the metric tensor g μ ν = e μ a e ν b η a b , {\displaystyle g_{\mu \nu }=e_{\mu }^{\;\

gravitation Jordan and Einstein frames – different conventions for the metric tensor, in a theory of a dilaton coupled to gravityPages displaying wikidata

not tied down to a special coordinate system. This description is a metric tensor at every point, or a connection which defines which nearby vectors are

connection and the basic tensors of General Relativity from a given metric tensor. Atlas 2 for Mathematica is a powerful Mathematica toolbox which allows

{\displaystyle M} with determinant | g | {\displaystyle |g|} of the metric tensor g {\displaystyle g} . The D = d + A {\displaystyle D=d+A} is the connection

abstract setting of category theory. Trace of a tensor with respect to a metric tensor Characteristic function Field trace Golden–Thompson inequality Singular

C^{2}} compact manifold with boundary with C 1 {\displaystyle C^{1}} metric tensor g {\displaystyle g} . Let Ω {\displaystyle \Omega } denote the manifold

{\displaystyle m} and charge e {\displaystyle e} , moving in a space with metric tensor g a b {\displaystyle g_{ab}} and electromagnetic field F a b {\displaystyle

a nearly static gravitational field, only the time component of the metric tensor is important, and the lowest order approximation is accurate enough

phase transitions, e.g., the scalar curvature of the thermodynamic metric tensor diverges at (and only at) a phase transition point. In the thermodynamic

-{\vec {\sigma }}).} and allow raising and lowering using the Minkowski metric tensor. The relation can then be written x ν = 1 2 tr ⁡ ( σ ¯ ν ( x μ σ μ )

derived from the formulas about hyperbolic triangles. The corresponding metric tensor field is: ( d s ) 2 = cosh 2 ⁡ y ( d x ) 2 + ( d y ) 2 {\displaystyle

where g μ ν {\displaystyle g^{\mu \nu }} are the components of the metric tensor and l μ {\displaystyle l^{\mu }} and n ν {\displaystyle n^{\nu }} are

function energy conversion efficiency efficiency (physics) the Minkowski metric tensor in relativity η-conversion in lambda calculus the learning rate in machine

the vierbein coordinate system, using roman-letter subscripts, the metric tensor is Euclidean: d s 2 = δ a b e a ⊗ e b = e 0 ⊗ e 0 + e 1 ⊗ e 1 + e 2

Approach to the Geometry of Brain Function: Cerebellar Coordination Via A Metric Tensor" (PDF). Neuroscience. 5 (7): 1125––1136. doi:10.1016/0306-4522(80)90191-8

solution of the field equations that describes the universe is the metric tensor called the Friedmann–Lemaître–Robertson–Walker metric, d s 2 = − c 2

representation in the brain. The cerebellum as a predictive space-time metric tensor". Neuroscience. 7 (12): 2949–70. doi:10.1016/0306-4522(82)90224-X. PMID 7162624

above proper acceleration 4-vector, to be found with the help of the metric tensor gij, is α = 1 / ( 1 − r s / r ) G M / r 2 {\textstyle \alpha ={\sqrt

Joos–Weinberg fields preferably couple to symmetric tensors, such as the metric tensor in gravity. Source: The ( 3 2 , 0 ) ⊕ ( 0 , 3 2 ) {\displaystyle \left({\tfrac

mass—fermion or otherwise—given by m2 = pσpσ, and employs a Minkowski metric tensor for which diag(η) = (+1, −1, −1, −1), it should be apparent that the

{\displaystyle f_{\mu \nu }} . The reference metric transforms like a metric tensor under diffeomorphism f μ ν → f μ ν ′ (   X ( x )   ) ≡ f α β   ∂ μ X

\sigma }+\eta _{\nu \sigma }M_{\mu \rho }\,} where η is the Minkowski metric tensor. (It is common to drop any hats for the four-momentum operators in the

respectively, one can then contract upper and lower indices (with the metric tensor) to obtain more interesting structures. For the quadratic Casimir invariant

Approach To The Geometry Of Brain Function: Cerebellar Coordination Via A Metric Tensor" (PDF). Neuroscience. 5 (7): 1125––1136. doi:10.1016/0306-4522(80)90191-8

symmetries generalise the action of the linearised diffeomorphisms from the metric tensor to higher-spin fields. In the context of gravity one may also be interested

(STF) polarization tensor P. In spherical polar coordinates (θ, ɸ), the metric tensor g and polarization tensor are: This matrix is symmetric and trace-free