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General relativity and Metric tensor (general relativity)

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between General relativity and Metric tensor (general relativity)

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

Similarities between General relativity and Metric tensor (general relativity)

General relativity and Metric tensor (general relativity) have 39 things in common (in Unionpedia): Abstract index notation, Alternatives to general relativity, Anti-de Sitter space, Connection (mathematics), Curvature, Einstein field equations, Energy, Euclidean space, Event horizon, Friedmann–Lemaître–Robertson–Walker metric, Gödel metric, General relativity, Gradient, Gravitational constant, Gravitational potential, Gravitational singularity, Gravity, Integrable system, Introduction to the mathematics of general relativity, Kerr metric, Levi-Civita connection, Mass, Matter, Minkowski space, Partial differential equation, Proper time, Pseudo-Riemannian manifold, Reissner–Nordström metric, Ricci calculus, Ricci curvature, ..., Riemann curvature tensor, Rindler coordinates, Scalar curvature, Schwarzschild metric, Spacetime, Special relativity, Stress–energy tensor, Tensor, Torsion tensor. Expand index (9 more) »

Abstract index notation

Abstract index notation is a mathematical notation for tensors and spinors that uses indices to indicate their types, rather than their components in a particular basis.

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Alternatives to general relativity

Alternatives to general relativity are physical theories that attempt to describe the phenomenon of gravitation in competition to Einstein's theory of general relativity.

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Anti-de Sitter space

In mathematics and physics, n-dimensional anti-de Sitter space (AdSn) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature.

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Connection (mathematics)

In geometry, the notion of a connection makes precise the idea of transporting data along a curve or family of curves in a parallel and consistent manner.

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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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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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Energy

In physics, energy is the quantitative property that must be transferred to an object in order to perform work on, or to heat, the object.

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Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

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Event horizon

In general relativity, an event horizon is a region in spacetime beyond which events cannot affect an outside observer.

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Friedmann–Lemaître–Robertson–Walker metric

The Friedmann–Lemaître–Robertson–Walker (FLRW) metric is an exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic, expanding or contracting universe that is path connected, but not necessarily simply connected.

Friedmann–Lemaître–Robertson–Walker metric and General relativity · Friedmann–Lemaître–Robertson–Walker metric and Metric tensor (general relativity) · See more »

Gödel metric

The Gödel metric is an exact solution of the Einstein field equations in which the stress–energy tensor contains two terms, the first representing the matter density of a homogeneous distribution of swirling dust particles (dust solution), and the second associated with a nonzero cosmological constant (see lambdavacuum solution).

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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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Gradient

In mathematics, the gradient is a multi-variable generalization of the derivative.

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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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Gravitational potential

In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that would be needed to move the object from a fixed reference location to the location of the object.

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Gravitational singularity

A gravitational singularity or spacetime singularity is a location in spacetime where the gravitational field of a celestial body becomes infinite in a way that does not depend on the coordinate system.

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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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Integrable system

In the context of differential equations to integrate an equation means to solve it from initial conditions.

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Introduction to the mathematics of general relativity

The mathematics of general relativity is complex.

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Kerr metric

The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially-symmetric black hole with a spherical event horizon.

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Levi-Civita connection

In Riemannian geometry, the Levi-Civita connection is a specific connection on the tangent bundle of a manifold.

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Mass

Mass is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied.

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Matter

In the classical physics observed in everyday life, matter is any substance that has mass and takes up space by having volume.

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Minkowski space

In mathematical physics, Minkowski space (or Minkowski spacetime) is a combining of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded.

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Partial differential equation

In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives.

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Proper time

In relativity, proper time along a timelike world line is defined as the time as measured by a clock following that line.

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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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Reissner–Nordström metric

In physics and astronomy, the Reissner–Nordström metric is a static solution to the Einstein-Maxwell field equations, which corresponds to the gravitational field of a charged, non-rotating, spherically symmetric body of mass M. The metric was discovered by Hans Reissner, Hermann Weyl, Gunnar Nordström and G. B. Jeffery.

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Ricci calculus

In mathematics, Ricci calculus constitutes the rules of index notation and manipulation for tensors and tensor fields.

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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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Riemann curvature tensor

In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the most common method used to express the curvature of Riemannian manifolds.

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Rindler coordinates

In relativistic physics, the coordinates of a hyperbolically accelerated reference frame constitute an important and useful coordinate chart representing part of flat Minkowski spacetime.

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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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Schwarzschild metric

In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild vacuum or Schwarzschild solution) is the solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assumption that the electric charge of the mass, angular momentum of the mass, and universal cosmological constant are all zero.

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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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Special relativity

In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time.

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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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Torsion tensor

In differential geometry, the notion of torsion is a manner of characterizing a twist or screw of a moving frame around a curve.

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The list above answers the following questions

General relativity and Metric tensor (general relativity) Comparison

General relativity has 366 relations, while Metric tensor (general relativity) has 82. As they have in common 39, the Jaccard index is 8.71% = 39 / (366 + 82).

References

This article shows the relationship between General relativity and Metric tensor (general relativity). To access each article from which the information was extracted, please visit:

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