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Einstein tensor

Index Einstein tensor

In differential geometry, the Einstein tensor (named after Albert Einstein; also known as the trace-reversed Ricci tensor) is used to express the curvature of a pseudo-Riemannian manifold. [1]

41 relations: Albert Einstein, Antisymmetric tensor, Bernard F. Schutz, Cambridge University Press, Christoffel symbols, Contracted Bianchi identities, Cosmological constant, Curvature, David Lovelock, Differentiable manifold, Differential equation, Differential geometry, Divergence, Einstein field equations, Einstein–Cartan theory, Gauss's law for gravity, General relativity, Geometrized unit system, Gravitational constant, Gravity, Inertial frame of reference, Killing vector field, Kronecker delta, Mathematics of general relativity, Metric tensor, Metric tensor (general relativity), Nonlinear system, Oxford University Press, Partial derivative, Prentice Hall, Pseudo-Riemannian manifold, Ricci curvature, Scalar curvature, Spacetime, Stress–energy tensor, Tensor, Tensor contraction, Trace (linear algebra), Vermeil's theorem, W. W. Norton & Company, Wolfgang Rindler.

Albert Einstein

Albert Einstein (14 March 1879 – 18 April 1955) was a German-born theoretical physicist who developed the theory of relativity, one of the two pillars of modern physics (alongside quantum mechanics).

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Antisymmetric tensor

In mathematics and theoretical physics, a tensor is antisymmetric on (or with respect to) an index subset if it alternates sign (+/−) when any two indices of the subset are interchanged.

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Bernard F. Schutz

Bernard F. Schutz (born August 11, 1946, in Paterson, New Jersey) is an American physicist.

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Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

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Christoffel symbols

In mathematics and physics, the Christoffel symbols are an array of numbers describing a metric connection.

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Contracted Bianchi identities

In general relativity and tensor calculus, the contracted Bianchi identities are: where _\mu is the Ricci tensor, R the scalar curvature, and \nabla_\rho indicates covariant differentiation.

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Cosmological constant

In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Λ) is the value of the energy density of the vacuum of space.

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Curvature

In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry.

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David Lovelock

David Lovelock (born 1938) is a British theoretical physicist and mathematician.

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Differentiable manifold

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.

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Differential equation

A differential equation is a mathematical equation that relates some function with its derivatives.

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Differential geometry

Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.

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Divergence

In vector calculus, divergence is a vector operator that produces a scalar field, giving the quantity of a vector field's source at each point.

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Einstein field equations

The Einstein field equations (EFE; also known as Einstein's equations) comprise the set of 10 equations in Albert Einstein's general theory of relativity that describe the fundamental interaction of gravitation as a result of spacetime being curved by mass and energy.

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Einstein–Cartan theory

In theoretical physics, the Einstein–Cartan theory, also known as the Einstein–Cartan–Sciama–Kibble theory, is a classical theory of gravitation similar to general relativity.

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Gauss's law for gravity

In physics, Gauss's law for gravity, also known as Gauss's flux theorem for gravity, is a law of physics that is essentially equivalent to Newton's law of universal gravitation.

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General relativity

General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.

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Geometrized unit system

A geometrized unit system or geometric unit system is a system of natural units in which the base physical units are chosen so that the speed of light in vacuum, c, and the gravitational constant, G, are set equal to unity.

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Gravitational constant

The gravitational constant (also known as the "universal gravitational constant", the "Newtonian constant of gravitation", or the "Cavendish gravitational constant"), denoted by the letter, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general theory of relativity.

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Gravity

Gravity, or gravitation, is a natural phenomenon by which all things with mass or energy—including planets, stars, galaxies, and even light—are brought toward (or gravitate toward) one another.

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Inertial frame of reference

An inertial frame of reference in classical physics and special relativity is a frame of reference in which a body with zero net force acting upon it is not accelerating; that is, such a body is at rest or it is moving at a constant speed in a straight line.

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Killing vector field

In mathematics, a Killing vector field (often just Killing field), named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo-Riemannian manifold) that preserves the metric.

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Kronecker delta

In mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers.

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Mathematics of general relativity

The mathematics of general relativity refers to various mathematical structures and techniques that are used in studying and formulating Albert Einstein's theory of general relativity.

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Metric tensor

In the mathematical field of differential geometry, a metric tensor is a type of function which takes as input a pair of tangent vectors and at a point of a surface (or higher dimensional differentiable manifold) and produces a real number scalar in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space.

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Metric tensor (general relativity)

In general relativity, the metric tensor (in this context often abbreviated to simply the metric) is the fundamental object of study.

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Nonlinear system

In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input.

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Oxford University Press

Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.

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Partial derivative

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary).

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Prentice Hall

Prentice Hall is a major educational publisher owned by Pearson plc.

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Pseudo-Riemannian manifold

In differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold in which the metric tensor need not be positive-definite, but need only be a non-degenerate bilinear form, which is a weaker condition.

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Ricci curvature

In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, represents the amount by which the volume of a small wedge of a geodesic ball in a curved Riemannian manifold deviates from that of the standard ball in Euclidean space.

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Scalar curvature

In Riemannian geometry, the scalar curvature (or the Ricci scalar) is the simplest curvature invariant of a Riemannian manifold.

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Spacetime

In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.

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Stress–energy tensor

The stress–energy tensor (sometimes stress–energy–momentum tensor or energy–momentum tensor) is a tensor quantity in physics that describes the density and flux of energy and momentum in spacetime, generalizing the stress tensor of Newtonian physics.

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Tensor

In mathematics, tensors are geometric objects that describe linear relations between geometric vectors, scalars, and other tensors.

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Tensor contraction

In multilinear algebra, a tensor contraction is an operation on a tensor that arises from the natural pairing of a finite-dimensional vector space and its dual.

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Trace (linear algebra)

In linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i.e., where aii denotes the entry on the ith row and ith column of A. The trace of a matrix is the sum of the (complex) eigenvalues, and it is invariant with respect to a change of basis.

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Vermeil's theorem

In differential geometry, Vermeil's theorem essentially states that the scalar curvature is the only (non-trivial) absolute invariant among those of prescribed type suitable for Einstein’s theory.

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W. W. Norton & Company

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Wolfgang Rindler

Wolfgang Rindler (born 18 May 1924, Vienna) is a physicist working in the field of General Relativity where he is known for introducing the term "event horizon", Rindler coordinates, and (in collaboration with Roger Penrose) for popularizing the use of spinors in general relativity.

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Einstein curvature tensor.

References

[1] https://en.wikipedia.org/wiki/Einstein_tensor

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