AI & ChatGPT searches , social queries for EINSTEIN TENSOR
Search references for EINSTEIN TENSOR. Phrases containing EINSTEIN TENSOR
See searches and references containing EINSTEIN TENSOR!
Search references for EINSTEIN TENSOR. Phrases containing EINSTEIN TENSOR
See searches and references containing EINSTEIN TENSOR!EINSTEIN TENSOR
Tensor used in general relativity
with conservation of energy and momentum. The Einstein tensor G {\displaystyle {\boldsymbol {G}}} is a tensor of order 2 defined over pseudo-Riemannian manifolds
Einstein_tensor
Field-equations in general relativity
tensor of spacetime for a given arrangement of stress–energy–momentum in the spacetime. The relationship between the metric tensor and the Einstein tensor
Einstein_field_equations
Tensor describing energy momentum density in spacetime
stress-energy tensor The stress–energy tensor, sometimes called the stress–energy–momentum tensor or the energy–momentum tensor, is a tensor field quantity
Stress–energy_tensor
Shorthand notation for tensor operations
the multiplication. Given a tensor, one can raise an index or lower an index by contracting the tensor with the metric tensor, g μ ν {\displaystyle g_{\mu
Einstein_notation
Measure of the curvature of a pseudo-Riemannian manifold
Riemann curvature tensor, the Weyl tensor expresses the tidal force that a body feels when moving along a geodesic. The Weyl tensor differs from the Riemann
Weyl_tensor
Algebraic object with geometric applications
(electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, etc.), and general relativity (stress–energy tensor, curvature tensor, etc.). In
Tensor
Tensor invariant under permutations of vectors it acts on
In mathematics, a symmetric tensor is an unmixed tensor that is invariant under a permutation of its vector arguments: T ( v 1 , v 2 , … , v r ) = T (
Symmetric_tensor
Tensor that describes the 4D geometry of spacetime
manifold M {\displaystyle M} and the metric tensor is given as a covariant, second-degree, symmetric tensor on M {\displaystyle M} , conventionally denoted
Metric tensor (general relativity)
Metric_tensor_(general_relativity)
the Ricci tensor. The Riemann curvature tensor can be expressed in terms of the covariant derivative. The Einstein tensor G is a rank-2 tensor defined over
Introduction to the mathematics of general relativity
Introduction_to_the_mathematics_of_general_relativity
Five-dimensional Einstein field equations
use the Kaluza–Klein–Einstein tensor, a generalization of the Einstein tensor, and can be obtained from the Kaluza–Klein–Einstein–Hilbert action, a generalization
Kaluza–Klein–Einstein field equations
Kaluza–Klein–Einstein_field_equations
{\displaystyle g^{il}W_{ijkl}=0} The Ricci tensor, the Einstein tensor, and the traceless Ricci tensor are symmetric 2-tensors: R j k = R k j {\displaystyle R_{jk}=R_{kj}}
List of formulas in Riemannian geometry
List_of_formulas_in_Riemannian_geometry
Tensor in differential geometry
relativity, the Ricci curvature tensor enters the Einstein field equations through the Einstein tensor, formed from the Ricci tensor, the scalar curvature, and
Ricci_curvature
Solution of Einstein field equations
solution, found in 1949 by Kurt Gödel, of the Einstein field equations in which the stress–energy tensor contains two terms: the first representing the
Gödel_metric
Aspect of general relativity
The Einstein tensor is built up from the metric tensor and its partial derivatives; thus, given the stress–energy tensor, the Einstein field equations
Solutions of the Einstein field equations
Solutions_of_the_Einstein_field_equations
Quantity in general relativity
of the Einstein tensor, G μ ν {\displaystyle G^{\mu \nu }} , with the stress–energy tensor, T μ ν {\displaystyle T^{\mu \nu }} by the Einstein field equations;
Stress–energy–momentum pseudotensor
Stress–energy–momentum_pseudotensor
Tensor field in Riemannian geometry
mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the
Riemann_curvature_tensor
Tensor equal to the negative of any of its transpositions
tensor is antisymmetric with respect to its first three indices. If a tensor changes sign under exchange of each pair of its indices, then the tensor
Antisymmetric_tensor
Operation in mathematics
In multilinear algebra, a tensor contraction is an operation on a tensor that arises from the canonical pairing of a vector space and its dual. This example
Tensor_contraction
Einstein tensor, computed uniquely from the metric tensor which is part of the definition of a Lorentzian manifold. Since giving the Einstein tensor does
Exact solutions in general relativity
Exact_solutions_in_general_relativity
Tensor having both covariant and contravariant indices
In tensor analysis, a mixed tensor is a tensor which is neither strictly covariant nor strictly contravariant; at least one of the indices of a mixed
Mixed_tensor
Theorem in general relativity
are the Einstein field equations. The theorem was described by British physicist David Lovelock in 1971. In four dimensional spacetime, any tensor A μ ν
Lovelock's_theorem
Assignment of a tensor continuously varying across a region of space
In mathematics and physics, a tensor field is a function assigning a tensor to each point of a region of a mathematical space (typically a Euclidean space
Tensor_field
Mathematical operation on vector spaces
two vectors is sometimes called an elementary tensor or a decomposable tensor. The elementary tensors span V ⊗ W {\displaystyle V\otimes W} in the sense
Tensor_product
Class of exact solutions to Einstein's field equations
}} , the viscous shear tensor is given by π μ ν {\displaystyle \pi ^{\mu \nu }} . The heat flux vector and viscous shear tensor are transverse to the world
Fluid_solution
Lorentzian manifold with vanishing Einstein tensor
fact that the Einstein tensor vanishes if and only if the Ricci tensor vanishes. This follows from the fact that these two second rank tensors stand in a
Vacuum_solution
Riemannian manifold which satisfies vacuum Einstein equations
mathematical physics, an Einstein manifold is a Riemannian or pseudo-Riemannian differentiable manifold whose Ricci tensor is proportional to the metric
Einstein_manifold
Branch of mathematics
various areas, including: Classical treatment of tensors Dyadic tensor Glossary of tensor theory Metric tensor Bra–ket notation Multilinear subspace learning
Multilinear_algebra
G_{ab}} is the Einstein tensor, Λ {\displaystyle \Lambda } is the cosmological constant, g a b {\displaystyle g_{ab}} is the metric tensor, c {\displaystyle
Mathematics of general relativity
Mathematics_of_general_relativity
Concept in mathematical physics
Lorentzian manifold in which the Einstein tensor is null. Such a spacetime can be interpreted as an exact solution of Einstein's field equation, in which the
Null_dust_solution
Tensor index notation for tensor-based calculations
notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection. It is also the modern
Ricci_calculus
of tensor theory. For expositions of tensor theory from different points of view, see: Tensor Tensor (intrinsic definition) Application of tensor theory
Glossary_of_tensor_theory
Antisymmetric permutation object acting on tensors
independent of any metric tensor and coordinate system. Also, the specific term "symbol" emphasizes that it is not a tensor because of how it transforms
Levi-Civita_symbol
Einstein field equation solution
solution is an exact solution to the Einstein field equation in which the only term in the stress–energy tensor is a cosmological constant term. This
Lambdavacuum_solution
Theory of gravitation as curved spacetime
is the Einstein tensor, G μ ν {\displaystyle G_{\mu \nu }} , which is symmetric and a specific divergence-free combination of the Ricci tensor R μ ν {\displaystyle
General_relativity
Mathematical object that describes the electromagnetic field in spacetime
electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a tensor that describes
Electromagnetic_tensor
Generalization of tensor fields
differential geometry, a tensor density or relative tensor is a generalization of the tensor field concept. A tensor density transforms as a tensor field when passing
Tensor_density
Classical theory of gravitation
formulation of spin (the spin tensor). These extra equations express the torsion linearly in terms of the spin tensor associated with the matter source
Einstein–Cartan_theory
Proposed theory of gravitation
Jordan–Brans–Dicke theory) is a competitor to Einstein's general theory of relativity. It is an example of a scalar–tensor theory, a gravitational theory in which
Brans–Dicke_theory
Algebraic operation on coordinate vectors
(single-) dot product between a tensor of order n {\displaystyle n} and a tensor of order m {\displaystyle m} is a tensor of order n + m − 2 {\displaystyle
Dot_product
represent ultraviolet corrections to Einstein theory, involving higher order contractions of the Riemann tensor Rμναβ. In particular, the second order
Lovelock_theory_of_gravity
Concept in general relativity
the metric tensor matrix, R {\displaystyle R} is the Ricci scalar, and κ = 8 π G c − 4 {\displaystyle \kappa =8\pi Gc^{-4}} is the Einstein gravitational
Einstein–Hilbert_action
Proposed theories of gravity
Einstein's general relativity is the simplest plausible theory of gravity that can be based on just one symmetric tensor field (the metric tensor).
Alternatives to general relativity
Alternatives_to_general_relativity
Decomposition in multilinear algebra
multilinear algebra, the tensor rank decomposition or rank-R decomposition is the decomposition of a tensor as a sum of R rank-1 tensors, where R is minimal
Tensor_rank_decomposition
Coordinate-free definition of a tensor
mathematics, the modern component-free approach to the theory of a tensor views a tensor as an abstract object, expressing some definite type of multilinear
Tensor_(intrinsic_definition)
Object in differential geometry
differential geometry, the torsion tensor is a tensor that is associated to any affine connection. The torsion tensor is a bilinear map of two input vectors
Torsion_tensor
Mathematical solution in general relativity
= 0 {\displaystyle {F^{jb}}_{;j}=0} The Einstein tensor must match the electromagnetic stress–energy tensor, G a b = 2 ( F a j F b j − 1 4 g a b F m
Electrovacuum_solution
Mathematical function of two variables; outputs 1 if they are equal, 0 otherwise
thought of as a tensor, and is written δ j i {\displaystyle \delta _{j}^{i}} . Sometimes the Kronecker delta is called the substitution tensor. When juxtaposition
Kronecker_delta
Scalar measure of the rotational inertia with respect to a fixed axis of rotation
inertia tensor of a body calculated at its center of mass, and R {\displaystyle \mathbf {R} } be the displacement vector of the body. The inertia tensor of
Moment_of_inertia
Graphical notation for multilinear algebra calculations
essentially the composition of functions. In the language of tensor algebra, a particular tensor is associated with a particular shape with many lines projecting
Penrose_graphical_notation
Mathematical notation for tensors and spinors
(a)\sigma (b)\sigma (c)}} Penrose graphical notation Einstein notation Index notation Tensor Antisymmetric tensor Raising and lowering indices Covariance and contravariance
Abstract_index_notation
Specification of a derivative along a tangent vector of a manifold
fields) and to arbitrary tensor fields, in a unique way that ensures compatibility with the tensor product and trace operations (tensor contraction). Given
Covariant_derivative
Electromagnetism in general relativity
of the source term in the Einstein field equations, the electromagnetic stress–energy tensor is a covariant symmetric tensor T μ ν = − 1 μ 0 ( F μ α g
Maxwell's equations in curved spacetime
Maxwell's_equations_in_curved_spacetime
Operation that pairs a left and a right R-module into an abelian group
universal property of the tensor product of vector spaces extends to more general situations in abstract algebra. The tensor product of an algebra and
Tensor_product_of_modules
Algebra associated to any vector space
alternating tensor subspace. On the other hand, the image A ( T ( V ) ) {\displaystyle {\mathcal {A}}(\mathrm {T} (V))} is always the alternating tensor graded
Exterior_algebra
Exterior algebraic map taking tensors from p forms to n-p forms
space L ( V , V ) {\displaystyle L(V,V)} is naturally isomorphic to the tensor product V ∗ ⊗ V ≅ V ⊗ V {\displaystyle V^{*}\!\!\otimes V\cong V\otimes
Hodge_star_operator
Isomorphism between the tangent and cotangent bundles of a manifold
index of an ( r , s ) {\displaystyle (r,s)} tensor gives a ( r − 1 , s + 1 ) {\displaystyle (r-1,s+1)} tensor, while raising an index gives a ( r + 1 ,
Musical_isomorphism
Field theory in physics that aims to unify the fundamental forces and particles
quanta are fermionic particles such as electrons, and tensor fields such as the metric tensor field that describes the shape of spacetime and gives rise
Unified_field_theory
Structure defining distance on a manifold
metric field on M consists of a metric tensor at each point p of M that varies smoothly with p. A metric tensor g is positive-definite if g ( v , v ) >
Metric_tensor
Physical theory with matter as quantum fields but gravity as a classical field
described by the semiclassical Einstein equations, which relate the curvature of spacetime that is encoded by the Einstein tensor G μ ν {\displaystyle G_{\mu
Semiclassical_gravity
Representation of mechanical stress at every point within a deformed 3D object
Cauchy stress tensor (symbol σ {\displaystyle {\boldsymbol {\sigma }}} , named after Augustin-Louis Cauchy), also called true stress tensor or simply stress
Cauchy_stress_tensor
Linear perturbations to solutions of nonlinear Einstein field equations
out using Einstein notation, hidden within the Ricci tensor and Ricci scalar are exceptionally nonlinear dependencies on the metric tensor that render
Linearized_gravity
Second order tensor in vector algebra
mathematics, specifically multilinear algebra, a dyadic or dyadic tensor is a second-order tensor, written in a notation that fits in with vector algebra. There
Dyadics
Unified field theory
Kaluza–Klein metric, the Kaluza–Klein–Einstein field equations, the equations of motion, the stress–energy tensor, and the cylinder condition. With no
Kaluza–Klein_theory
Physical constant for the strength of gravity induced by a mass
Gμν is the Einstein tensor (not the gravitational constant despite the use of G), Λ is the cosmological constant, gμν is the metric tensor, Tμν is the
Gravitational_constant
Term in differential geometry
curvature tensor, i.e. R ( X , Y ) = Ω ( X , Y ) , {\displaystyle \,R(X,Y)=\Omega (X,Y),} using the standard notation for the Riemannian curvature tensor. If
Curvature_form
Theory of interwoven space and time by Albert Einstein
scientific theory of the relationship between space and time. In Albert Einstein's 1905 paper, "On the Electrodynamics of Moving Bodies", the theory is presented
Special_relativity
Universal construction in multilinear algebra
the tensor algebra of a vector space V, denoted T(V) or T•(V), is the algebra of tensors on V (of any order) with multiplication being the tensor product
Tensor_algebra
Branch of mathematics
emergence of Einstein's theory of general relativity and the importance of the Einstein Field equations. Einstein's theory popularised the tensor calculus
Differential_geometry
Array of numbers describing a metric connection
corresponding gravitational potential being the metric tensor. When the coordinate system and the metric tensor share some symmetry, many of the Γijk are zero
Christoffel_symbols
Vector behavior under coordinate changes
consequently a vector is called a contravariant tensor. A vector, which is an example of a contravariant tensor, has components that transform inversely to
Covariance and contravariance of vectors
Covariance_and_contravariance_of_vectors
Attraction of masses and energy
}=\kappa T_{\mu \nu },} where Gμν is the Einstein tensor, gμν is the metric tensor, Tμν is the stress–energy tensor, Λ is the cosmological constant, G {\displaystyle
Gravity
Tensor operator generalizes the notion of operators which are scalars and vectors
graphics, a tensor operator generalizes the notion of operators which are scalars and vectors. A special class of these are spherical tensor operators which
Tensor_operator
Mathematical Concept
notation is as follows: Write down the second order tensor in matrix form (in the example, the stress tensor) Strike out the diagonal Continue on the third
Voigt_notation
Ways of writing certain laws of physics
t^{2}}-\nabla ^{2}.} The signs in the following tensor analysis depend on the convention used for the metric tensor. The convention used here is (+ − − −), corresponding
Covariant formulation of classical electromagnetism
Covariant_formulation_of_classical_electromagnetism
Second-rank tensor in quantum chromodynamics
In theoretical particle physics, the gluon field strength tensor is a second-order tensor field characterizing the gluon interaction between quarks. The
Gluon_field_strength_tensor
German-born theoretical physicist (1879–1955)
written in April 1953. Bern Historical Museum – Einstein Museum Einstein notation – Shorthand notation for tensor operations Frist Campus Center at Princeton
Albert_Einstein
Type of exact solution in general relativity of Einstein's field equations
b = 0 {\displaystyle g^{ab}\psi _{;ab}=0} , The Einstein tensor must match the stress-energy tensor for the scalar field, which in the simplest case
Scalar_field_solution
Topological space that locally resembles Euclidean space
tensor Weyl tensor Physics Moment of inertia Angular momentum tensor Spin tensor Cauchy stress tensor stress–energy tensor Einstein tensor EM tensor Gluon field
Manifold
Identities in general relativity
identities Einstein tensor Einstein field equations General theory of relativity Ricci calculus Tensor calculus Riemann curvature tensor Bianchi, Luigi
Contracted_Bianchi_identities
Type of physical quantity
spacetime Tensor – Algebraic object with geometric applications Tensor density – Generalization of tensor fields Tensor field – Assignment of a tensor continuously
Pseudotensor
Spinning motion in theoretical physics
theoretical physics, the spin tensor is a quantity used to describe the rotational motion of particles in spacetime. The spin tensor has application in general
Spin_tensor
Theory of gravity by Albert Einstein
geometrical quantity G, now called the Einstein tensor, which describes some aspects of the way spacetime is curved. Einstein's equation then states that G = 8
Introduction to general relativity
Introduction_to_general_relativity
Covariant derivative of the metric tensor
In mathematics, the nonmetricity tensor in differential geometry is the covariant derivative of the metric tensor. It can be interpreted as the failure
Nonmetricity_tensor
Differential form of degree one or section of a cotangent bundle
one coordinate system to another. Thus a one-form is an order 1 covariant tensor field. The most basic non-trivial differential one-form is the "change in
One-form
Concept in mathematics
In mathematics, the tensor bundle of a manifold is the direct sum of all tensor products of the tangent bundle and the cotangent bundle of that manifold
Tensor_bundle
Hypothetical topological feature of spacetime
manifold of Einstein's field equations for a vacuum spacetime, modified by inclusion of a scalar field minimally coupled to the Ricci tensor with antiorthodox
Wormhole
Affine connection on the tangent bundle of a manifold
components of a contravariant vector. This discovery was the real beginning of tensor analysis. In 1906, L. E. J. Brouwer was the first mathematician to consider
Levi-Civita_connection
Conserved physical quantity; rotational analogue of linear momentum
as an anti-symmetric second order tensor, with components ωij. The relation between the two anti-symmetric tensors is given by the moment of inertia which
Angular_momentum
radius Einstein group Einstein ring Einstein–Infeld–Hoffmann equations Einstein synchronisation Einstein tensor Einstein zigzag Einstein's static universe Friedmann–Einstein
List of things named after Albert Einstein
List_of_things_named_after_Albert_Einstein
electromagnetic tensor and where η μ ν {\displaystyle \eta _{\mu \nu }} is the Minkowski metric tensor of metric signature (− + + +) and the Einstein summation
Electromagnetic stress–energy tensor
Electromagnetic_stress–energy_tensor
Theory of gravity
it identically vanishes. Despite being quadratic in the Riemann tensor (and Ricci tensor), terms containing more than 2 partial derivatives of the metric
Gauss–Bonnet_gravity
Assignment of numbers to points in space
tensor field called Einstein tensor. In Kaluza–Klein theory, spacetime is extended to five dimensions and its Riemann curvature tensor can be separated out
Scalar_field
Branch of physics which studies the behavior of materials modeled as continuous media
stress tensor, and ρ 0 {\displaystyle \rho _{0}} is the mass density in the reference configuration. The first Piola-Kirchhoff stress tensor is related
Continuum_mechanics
Hypothetical elementary particle that mediates gravity
stress–energy tensor, a second-order tensor (compared with electromagnetism's spin-1 photon, the source of which is the four-current, a first-order tensor). Additionally
Graviton
Non-tensorial representation of the spin group
distinguished from the tensor representations given by Weyl's construction by the weights. Whereas the weights of the tensor representations are integer
Spinor
Abbreviation in the fields of special and general relativity
relativity, a four-tensor is an abbreviation for a tensor in a four-dimensional spacetime. General four-tensors are usually written in tensor index notation
Four-tensor
Array of numbers
multiplication can be defined with entries objects of a category equipped with a "tensor product" similar to multiplication in a ring, having coproducts similar
Matrix_(mathematics)
Type of derivative in differential geometry
differentiable manifold. Functions, tensor fields and forms can be differentiated with respect to a vector field. If T is a tensor field and X is a vector field
Lie_derivative
Class of exact solutions to Einstein's field equations
^{4}+a_{3}\,\lambda ^{3}+a_{2}\,\lambda ^{2}+a_{1}\,\lambda +a_{0}} of the Einstein tensor in a dust solution will have the form χ ( λ ) = ( λ − 8 π μ ) λ 3
Dust_solution
Measure of curvature in differential geometry
the fundamental terms in the Einstein field equation. However, unlike the Riemann curvature tensor or the Ricci tensor, the scalar curvature cannot be
Scalar_curvature
EINSTEIN TENSOR
EINSTEIN TENSOR
Boy/Male
Norse
Lucky.
Boy/Male
Norse
Rock or hard spear.
Boy/Male
Norse
Lucky.
Surname or Lastname
English
English : unexplained.Possibly an Americanized spelling of French Imbert or a translation of German and Jewish Bernstein, which means ‘amber’.Muslim (widespread throughout the Muslim world) : from the Arabic personal name ‛Anbar, literally ‘perfume’, ‘ambergris’, figuratively ‘good’, ‘pleasant’, ‘agreeable’.
Surname or Lastname
English
English : from an Old English personal name composed of the elements wynn ‘joy’ + stÄn ‘stone’.English : habitational name from any of various places called Winston or Winstone, from various Old English personal names + Old English tÅ«n ‘enclosure’, ‘settlement’, or, in the case of Winstone in Gloucestershire, Old English stÄn ‘stone’.Americanized form of Jewish Weinstein.
Surname or Lastname
English
English : habitational name from any of various places called Burston, in Buckinghamshire, Norfolk, and Staffordshire, which have different origins. The Buckinghamshire place name is from an Old English personal name Briddel + Old English þorn ‘thorn tree’; the place in Norfolk is named with Old English byrst ‘rough ground’, ‘landslip’ + tÅ«n ‘farmstead’; the Staffordshire place name has the same second element, the first being an Old English personal name Burgwine or Burgwulf.English : possibly from an unrecorded Old English personal name, BurgstÄn.Jewish (American) : Americanized spelling of Burstein (see Bernstein).
EINSTEIN TENSOR
EINSTEIN TENSOR
Boy/Male
Hawaiian
Style.
Male
Finnish
Finnish form of Greek Ieremias (Hebrew Yirmeyahu), JORMA means "Jehovah casts forth" or "Jehovah hurls."
Girl/Female
Biblical
Grief, trouble.
Male
Hindi/Indian
(पà¥à¤°à¤¤à¤¾à¤ª) Hindi name PRATAP means "dignity, majesty."
Boy/Male
Tamil
Polite
Male
English
Middle English form of Anglo-Saxon Siweard, SIWARD means "sea-guard."
Girl/Female
Hindu, Indian, Marathi, Sanskrit
Honour; Pride; Goddess Durga
Girl/Female
Indian, Sanskrit
Garlanded with the Salmali Trees
Boy/Male
Bengali, Hindu, Indian
Certain; Eternal
Boy/Male
Celebrity, Indian, Malayalam
Lord Ganesha
EINSTEIN TENSOR
EINSTEIN TENSOR
EINSTEIN TENSOR
EINSTEIN TENSOR
EINSTEIN TENSOR
n.
The ratio of one vector to another in length, no regard being had to the direction of the two vectors; -- so called because considered as a stretching factor in changing one vector into another. See Versor.
n.
A muscle that stretches a part, or renders it tense.