An Etymological Dictionary of Astronomy and Astrophysics
English-French-Persian

A → tensor of → weight  → zero.

→ absolute; → tensor.

The branch of mathematics dealing with the differentiation of tensors.

→ calculus; → tensor.

Afmârik, → calculus; → tensor.

A tensor whose components are distinguished by → superscript indices.

→ contra-; + variant; → variance; → tensor.

A tensor whose components are distinguished by → subscript indices.

→ covariant; → tensor.

A mathematical entity describing the → curvature of → space-time in → Einstein's field equations, according to the theory of → general relativity. It is expressed by G_μν = R_μν - (1/2) g_μνR, where R_μν is the Ricci tensor, g_μν is the → metric tensor, and R the scalar curvature. This tensor is both symmetric and divergence free.

Named after Albert Einstein (1879-1955); → tensor.

A tensor (T_μν) related to the → Einstein tensor through → Einstein's field equations. The energy-momentum tensor depends upon the distribution of the → energy and → matter in the space.

→ energy; → momentum; → tensor.

The abstract tensor operation which is computed in a particular → reference frame using the → metric components. The metric tensor defines magnitude and direction of vectors about a point.

→ metric; → tensor.

The maximum number of the indices (→ index) of a tensor.

→ order; → tensor.

A generalized tensor concept that is characterized by a → Jacobian matrix of transformation raised to a power called → weight of a tensor density. In practice, only relative tensors of weight 1 or -1 are used. The product of a relative tensor of weight -1 by another tensor of weight 1 is an → absolute tensor. Same as → tensor density.

→ relative; → tensor.

A → rank 2, → symmetric tensor R_μν that is a contraction of the → Riemann curvature tensor R^λ_μνλ. More specifically, R_μν ≡ Σ (λ) R^λ_μνκ = R^λ_μνκ. Closely related to the Ricci tensor is the → Einstein tensor, which plays an important role in the theory of → general relativity.

Named after the Italian mathematician Gregorio Ricci-Curbastro (1853-1925); → tensor.

A 4th → rank tensor that characterizes the deviation of the geometry of space from the Euclidean type. The curvature tensor R^λ_μνκ is defined through the → Christoffel symbols Γ^λ_μν as follows: R^λ_μνκ = (∂Γ^λ_μκ)/(∂x^ν) - (∂Γ^λ_μν)/(∂x^κ) + Γ^η_μκΓ^λ_ην - Γ^η_μνΓ^λ_ηκ.

→ Riemannian geometry; → curvature; → tensor.

An alternative to the standard → general relativity of gravity that contains not only the → tensor field (or → metric), but also a → scalar field. In this formalism, the → gravitational constant is considered to vary over time. As a consequence, the measured strength of the gravitational interaction is a function of time. Same as → Jordan-Brans-Dicke theory.

→ scalar; → tensor; → theory.

A tensor that is the negative of its → transpose. For example, a second-order covariant tensor A_jk if its components satisfy the equality: A_jk = - A_kj. Also called antisymmetric tensor.

→ skew; → symmetric; → tensor.

Tânsor, → tensor; pâd-, → anti-; hamâmun, → symmetric.

A tensor that is → invariant under any → permutation of its indices (→ index). In other words, a tensor that equals its → transpose. For example, a second-order → covariant tensor A_jk if its components satisfy the equality: A_jk = A_kj.

→ symmetric; → tensor.

A system of numbers or functions where components obey a certain law of transformation when the variables undergo a linear transformation. A tensor may consist of a single number, in which case it is referred to as a tensor of order zero, or simply a → scalar. The tensor of order one represents a → vector. Similarly there will be tensors of order two, three, and so on.
See also:
→ absolute tensor, → calculus of tensors, → contravariant tensor, → covariant tensor, → Einstein tensor, → energy-momentum tensor, → metric tensor, → order of a tensor, → relative tensor, → Ricci tensor, → Riemann curvature tensor, → scalar-tensor theory, → skew-symmetric tensor, → symmetric tensor, → tensor analysis, → tensor contraction, → tensor density, → tensor field, → tensor perturbation, → tensor rank, → tensor-vector-scalar (TeVeS) theory, → weight of a tensor.

Agent noun of tense (v.) → tension.

A method of calculation in higher mathematics based on the properties of tensors.

→ tensor; → analysis.

An operation of tensor algebra that is obtained by setting unlike indices equal and summing according to a summation convention.

→ contraction; → tensor.

A generalization of the tensor concept that like a tensor transforms, except for the appearance of an extra factor, which is the → Jacobian matrix of the transformation of the coordinates, raised to some power, in transformation law. The exponent, which is a positive or negative integer, is called the weight of the tensor density. → weight of a tensor density. Ordinary tensors are tensor densities of weight 0. Tensor density is also called → relative tensor.

→ tensor; → density.

A field of space and time each point of which has multiple directionality, and is describable by a tensor function.

→ tensor; → field.

The perturbation in the → primordial Universe plasma caused by → gravitational waves. These waves stretch and squeeze space in orthogonal directions and bring about → quadrupole anisotropy in incoming radiation temperature.

→ tensor; → perturbation.